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<h2 class="hd hd-2 unit-title">Resource Index</h2>
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<p>This resource index gives users access to most of the course resources in a single location.</p>
<h2>Unit I: Ax = b and the Four Subspaces</h2>
<table>
<thead>
<tr><th scope="col"><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]">TITLES</a></th><th scope="col"><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]">LECTURE VIDEOS</a></th><th scope="col"><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]">LECTURE NOTES</a></th><th scope="col"><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]">PROBLEM SOLVING VIDEOS</a></th><th scope="col"><nobr>PROBLEM</nobr><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]"> SETS</a></th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]">The Geometry of Linear Equations</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/62473e61830a440f8c1fbe5fa6d214ad" target="[object Object]">The Geometry of Linear Equations (00:39:49)</a></td>
<td><a href="/assets/courseware/v1/ae02ce3639cbdf5a8a41bd9d331e3645/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.1_GeoLE_LecSum.pdf" target="[object Object]">Lecture Summary (PDF)</a></td>
<td>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/fb3f9d1af7d34003b446fe9981136215" target="[object Object]">Geometry of Linear Algebra (00:16:35)</a></p>
<a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/5f3ac32298ca4144be5743f76e417cc7" target="[object Object]">The Geometry of Linear Algebra Chinese 线性代数的几何表示 (00:15:34)</a></td>
<td>
<p><a href="/assets/courseware/v1/f040db351f894a219a50beb0e7d71785/asset-v1:OCW+18.06SC+2T2019+type@asset+block/MIT18_06SCF11_Ses1.1prob.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/b094b9330002e4b4f1c53e2f7873fe50/asset-v1:OCW+18.06SC+2T2019+type@asset+block/MIT18_06SCF11_Ses1.1sol.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/18af0c82397e4c4badf404aedfd05e32" target="[object Object]">An Overview of Key Ideas</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ce0dad5562da4567ac24603cf4b1a0ae " target="[object Object]">An Overview of Linear Algebra (00:49:32)</a></td>
<td><a href="/assets/courseware/v1/4fe9707db6f2133f6e226f8e148c06ec/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Overview_KI_1.2_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b54f41e1ff0c459f876453703b47e1d1" target="[object Object]">An Overview of Key Ideas (00:07:42)</a></td>
<td>None</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/89625951dcc242c4a2dccd3d4ade3d8e" target="[object Object]">Elimination with Matrices</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/38dc2d6f0a284562ae3c81814600972b" target="[object Object]">Elimination with Matrices (00:47:42) </a></td>
<td><a href="/assets/courseware/v1/f5ebd5160a6aded1020ab6b3d19c885c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.3_Lecture_Summary_EWM.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/324109eb0a084882bdac6de303c62f9d" target="[object Object]">Elimination with Matrices (00:10:13)</a></td>
<td>
<p><a href="/assets/courseware/v1/f2f59ed6cea95c9e897a77b2ec0dc17d/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.3_Exercises_EWM.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/457cdfef9e8a5892b02eea87282a97c9/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.3_Solutions_EWM.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
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<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/9f5cb75b5e77491e942c7ba71b690897" target="[object Object]">Multiplication and Inverse Matrices</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/90e6e8c1a1874474aa1b396725fa3a9c" target="[object Object]">Multiplication and Inverse Matrices (00:46:49)</a></td>
<td><a href="/assets/courseware/v1/8d7985fd5d8a95db644a907e2970b298/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.4_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/9274a62e9124499bbc142b0678b19b9a" target="[object Object]">Inverse Matrices (00:08:24)</a></td>
<td>
<p><a href="/assets/courseware/v1/00653c39ccaea59471150735856b6652/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.4_Problems.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/e038d2d9aa03bae7f9475725deec7a12/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.4_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
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<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/bf060b5a522e479fabb3876b5287e289" target="[object Object]">Factorization into A = LU</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/690f0a541e924249ab07a7025fa407e5" target="[object Object]">Factorization into A = LU (00:50:13)</a></td>
<td><a href="/assets/courseware/v1/93a3d508b63e3792c7e17778d29fb595/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.5_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/a6cc452e4d334886ada2cf9787c0d85d" target="[object Object]">LU Decomposition (00:09:33)</a></td>
<td>
<p><a href="/assets/courseware/v1/679fc5c09c516b14f1f58ae5ecea1ea7/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.5_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/630be9bd0a2bbb6cb79eadb81a9920c3/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.5_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
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<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/a43bb7c37a88414fb131572b25aedc7f" target="[object Object]">Transposes, Permutations, Vector Spaces</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/e6d34fc4d39445128555ab615e8a5873" target="[object Object]">Transposes, Permutations, Vector Spaces (00:47:42) </a></td>
<td><a href="/assets/courseware/v1/fafd91f64f9084eade542f0efc2a76b3/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.6_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/8b69cc84e8e04fefb88f56e7d7821a0b" target="[object Object]">Subspaces of Three Dimensional Space (00:14:44)</a></p>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c93b2e067982458683d0cc3c91cf567b" target="[object Object]">三维空间的子空间 (00:13:07)</a></p>
</td>
<td>
<p><a href="/assets/courseware/v1/b629d4e8893f9fb4a21c314483ed3f02/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.6_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/c5b4625d4b9ba6296afb52866b5dd6ea/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.6_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
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<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/77f805cd496542a3b8da64cb24b00d58" target="[object Object]">Column Space and Nullspace</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/e49ddee05be64da09fcf1b3e34894e7d" target="[object Object]">Column Space and Nullspace (00:46:01)</a></td>
<td><a href="/assets/courseware/v1/0961f01909342320f1d3daaa1750055f/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.7_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/52dfb935bb77425c9509dfe83571c6fb" target="[object Object]">Vector Subspaces (00:08:45)</a></td>
<td>
<p><a href="/assets/courseware/v1/a767bce104aef9843324c7635f6b44d8/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.7_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/5e2d6ac93929db78d36a411256b3ce69/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.7_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/97f7e038ae494b18915767e805a2bd98" target="[object Object]">Solving Ax = 0: Pivot Variables, Special Solutions</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4b8e040dd3c0423c90960c13ed7ee608" target="[object Object]">Solving Ax = 0: Pivot Variables, Special Solutions (00:43:20) </a></td>
<td><a href="/assets/courseware/v1/62575073bfbb6c92733fb6c8c28f708c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.8_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/48666385f6d848bfb20fb83b1f3e3bf7" target="[object Object]">Solving Ax=0 (00:10:03) </a></td>
<td>
<p><a href="/assets/courseware/v1/47912230232aba265803b399856176c4/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.8_Problems.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/cc4a6795b78d233f5f3c00d1cced83ee/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.8_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/236c988e7fcd407283b94461363330bb" target="[object Object]">Solving Ax = b: Row Reduced Form R</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/7206fbbafc7f451995a51c6a22862180" target="[object Object]">Solving Ax = b: Row Reduced Form R (00:47:20)</a></td>
<td><a href="/assets/courseware/v1/f84a01e06b6fd0c34cd686c6b143ef2e/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.9_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/86a59c13a8ab425c8bc065ff6dd1a703" target="[object Object]">Solving Ax=b (00:09:03)</a></td>
<td>
<p><a href="/assets/courseware/v1/d885df8a1aeeb1f514f9d89f5618f85e/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.9_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/65d512eb10210845ae9e71b06fa4e293/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_1.9_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/0fc47a9bb9eb4d8d9eff028df12687cf" target="[object Object]">Independence, Basis and Dimension</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/aa28edb0ea1d4e4399a1bc9bf21cf8d0" target="[object Object]">Independence, Basis and Dimension (00:50:14)</a></td>
<td><a href="/assets/courseware/v1/d7f07b513167005eca28f5ae423db1db/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.0_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/916c7ef37eba4cc5ab16dc2466de2514" target="[object Object]">Basis and Dimension (00:08:09)</a></td>
<td>
<p><a href="/assets/courseware/v1/ba78a0ec35be7cbb8e6b6c9a2f187958/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.0_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/176e06498b7c548eff14c73f8e82a17b/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.0_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/67cb6f1344ae4b69939d92b0bcafac37" target="[object Object]">The Four Fundamental Subspaces</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/201c30a2413a493784ce407acbc21e5e" target="[object Object]">The Four Fundamental Subspaces (00:49:20)</a></td>
<td><a href="/assets/courseware/v1/6f5828ccd9e3880068960712d84e618a/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.1_LecSum.pdf" target="[object Object]">Lecture summary (PDF) </a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4dd8515d16ab425695c6aa2990d2ed3a" target="[object Object]">Computing the Four Fundamental Subspaces (00:10:44)</a></td>
<td>
<p><a href="/assets/courseware/v1/76262562b21dedb90d0264b8912fde45/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.1_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/55b2e9608fb8e18d6fe79dc9d2465d46/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.1_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/cac032ead5304015bbd26d24600566f3" target="[object Object]">Matrix Spaces; Rank 1; Small World Graphs</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/d7b2146689bc4474817e28788b604e39 " target="[object Object]">Matrix Spaces; Rank 1; Small World Graphs (00:45:56)</a></td>
<td><a href="/assets/courseware/v1/d5fbdd0aa675c742cb338654098b61d0/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.2_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/9a39eadada694fcb9baef5b87ef58afe" target="[object Object]">Matrix Spaces (00:08:55)</a></td>
<td>
<p><a href="/assets/courseware/v1/66fdec4b2aa55ffcf5d67f5c77a767a5/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.2_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/09ed4be45ace38c2d4f2a8e61236198f/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.2_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/15b479b3f3384243a1eb1d5d62ab4ad7" target="[object Object]">Graphs, Networks, Incidence Matrices</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/45113d95de654c93aafb804db64fff76" target="[object Object]">Graphs, Networks, Incidence Matrices (00:47:57)</a></td>
<td><a href="/assets/courseware/v1/b448f54b965be71a70d6bb2e9bd6e4b7/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c1fae46167ef470695015c5df649c4fc" target="[object Object]">Graphs and Networks (00:12:30)</a></td>
<td>
<p><a href="/assets/courseware/v1/30d1abbc2aca814e3076c872569059bd/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/226dc6d7a91418c3cf2a073ac583039d/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/1c0d69bb39674f84a5eb971112f11e7c " target="[object Object]">Exam 1 Review</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/8c76cf714bd449cd8783eb10f1937a05" target="[object Object]">Exam 1 Review (00:47:40)</a></td>
<td><a href="/assets/courseware/v1/84e30c5e083631f70982b5b532ab92ac/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.4_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c28bab0358754e67966038f763ff22df" target="[object Object]">Exam 1 Problem Solving (00:14:52)</a></td>
<td>None</td>
</tr>
</tbody>
</table>
<h2>Exam 1</h2>
<table>
<thead>
<tr><th scope="col">EXAM</th><th scope="col">EXAMS AND SOLUTIONS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/54b54a3ae79a4d43a93f415e6e470302" target="[object Object]">Exam 1</a></td>
<td>
<p><a href="/assets/courseware/v1/50e7815da13a7e260d2452ee33f5c5e4/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.5_Exam_1.pdf" target="[object Object]">Exam (PDF)</a></p>
<p><a href="/assets/courseware/v1/6196fceb9794c67d9dbed49b5277a0cb/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.5_Exam_1_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
</tbody>
</table>
<h2>Unit II: Least Squares, Determinants and Eigenvalues</h2>
<table>
<thead>
<tr><th scope="col">TITLES</th><th scope="col">LECTURE VIDEOS</th><th scope="col"><nobr>LECTURE</nobr> NOTES</th><th scope="col">PROBLEM SOLVING VIDEOS</th><th scope="col"><nobr>PROBLEM</nobr> SETS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ed1f679441524d7a9e7db385db508982" target="[object Object]">Orthogonal Vectors and Subspaces</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/e3733151dc2b499190a83913028deb0c" target="[object Object]">Orthogonal Vectors and Subspaces (00:49:48)</a></td>
<td><a href="/assets/courseware/v1/74f6011c0f66cbdbd5835c48ace0c614/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.1sum.pdf" target="[object Object]">Lecture Summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/5d9e01589ac24f899c043de9704bc21d " target="[object Object]">Orthogonal Vectors and Subspaces (00:10:19)</a></td>
<td>
<p><a href="/assets/courseware/v1/96e2889c0c30287848d4e38d8ebdbf50/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.1_Problems.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/d334482c56377e0797b9ee1a5148940c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.1_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4ded430a602f4ee39fd7e86f97b1bf95" target="[object Object]">Projections onto Subspaces</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/7b9aa1a92bb0413ca5f9186b68e345a6" target="[object Object]">Projections onto Subspaces (00:48:51)</a></td>
<td><a href="/assets/courseware/v1/fe6c9742b95701187e423306f7248d70/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.2_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/836604e9f30a4f9f802651a430a36846" target="[object Object]">Projections onto Subspaces (00:09:50)</a></td>
<td>
<p><a href="/assets/courseware/v1/d905f0ca49bad78c0a47f079a5edc5a5/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.2_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/4c717899b94af23a4119d3492812a667/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.2_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/a77018d846a043899b17157d7fc772d6" target="[object Object]">Projection Matrices and Least Squares</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/d8a02abbb87c415487ee6aae39db2680" target="[object Object]">Projection Matrices and Least Squares (00:48:05)</a></td>
<td><a href="/assets/courseware/v1/22528fa40a16b8dbbeeec49096ad5d52/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.3_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ab2e75dd871b4bf2866db9f9dcf93883" target="[object Object]">Least Squares Approximation (00:08:03)</a></td>
<td>
<p><a href="/assets/courseware/v1/101bf83b70192d145f37211f18cebebf/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.3_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/b81a41b16382271fa9a9180fdae7f422/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.3_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/3f5f21368ae4480682d29c99ef2516ad" target="[object Object]">Orthogonal Matrices and Gram-Schmidt</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/3bb62ecbf5624a8eaa20637b888f7ee5" target="[object Object]">Orthogonal Matrices and Gram-Schmidt (00:49:25)</a></td>
<td><a href="/assets/courseware/v1/9074eb57b9f310712ae05ffbd4f35608/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.4_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ca88818f22244cafa0187a5130e17dfc" target="[object Object]">Gram-Schmidt Orthogonalization (00:09:59)</a></td>
<td>
<p><a href="/assets/courseware/v1/9f29db092652076764a2790658d37411/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.4_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/87293feade49025731d68b25c37f8d00/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.4_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/2857c0f90e16482a80f5da0495d1f889" target="[object Object]">Properties of Determinants</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/d2c62db204d54cc3ac80be7190e521b5" target="[object Object]">Properties of Determinants (00:49:12)</a></td>
<td><a href="/assets/courseware/v1/9896efdb834af6f3716a105bdab79b0f/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.5_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/30003675799d4f5ea122ffc6dc50df3b" target="[object Object]">Properties of Determinants (00:09:55)</a></td>
<td>
<p><a href="/assets/courseware/v1/16fda56dcc88d49216e66771dac9cb9e/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.5_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/3752f3c59dd22327440e61e100c37bb6/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.5_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/be00d75b541d4e20a28d11662edbde71" target="[object Object]">Determinant Formulas and Cofactors</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b7919f9f94d04d1480cc13c9d6d47c78" target="[object Object]">Determinant Formulas and Cofactors (00:53:17)</a></td>
<td><a href="/assets/courseware/v1/109e71bdf7eac7d6bb13a2681adad419/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.6Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/23de0c8c77734b6cb7e9823be88811dc" target="[object Object]">Determinants (00:12:48)</a></p>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/74a756bfd8d34088a3c29d637bc08c71" target="[object Object]">行列式 (00:12:08) </a></p>
</td>
<td>
<p><a href="/assets/courseware/v1/8aff0a86312647fb3fdba5c22225539c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.6_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/ff85d462398b21aa60ffeeda5b2bec7d/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.6_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ae215febd2f74790bfd7d01bfdc65ddd" target="[object Object]">Cramer's Rule, Inverse Matrix and Volume</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/6fe059e159b840d19a287ee362adbafb" target="[object Object]">Cramer's Rule, Inverse Matrix and Volume (00:51:01)</a></td>
<td><a href="/assets/courseware/v1/425dda0f0f6d34033d49d58c05f256ff/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.7_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/9783aedc762e42b88ddaa46bac98ba33" target="[object Object]">Determinants and Volume (00:13:49)</a></p>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/9f6db700081344a98e406b74c23b9d4e" target="[object Object]">行列式和体积 (00:11:33)</a></p>
</td>
<td>
<p><a href="/assets/courseware/v1/c92f0f4955a04d45a2dd4b65ca3024ff/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.7_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/eb90fd1ec1081b4f0e8aa00b55a8978c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.7_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/2d7457518a924a5989c46c17ec4d1bb6" target="[object Object]">Eigenvalues and Eigenvectors</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/a61213a20e62427fa70725fe5e526125" target="[object Object]">Eigenvalues and Eigenvectors (00:51:23)</a></td>
<td><a href="/assets/courseware/v1/6c29d20a4e6265da1c236d9930135a2f/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.8_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b2525063d4bb4322bc9cdc2bf15da9db" target="[object Object]">Eigenvalues and Eigenvectors (00:09:21)</a></td>
<td>
<p><a href="/assets/courseware/v1/f6e78978df641da5745e5605a557b6e1/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.8_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/e46df31fea262c131266d5eef08e4473/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.8_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ac556a8b38cc4980ba5b727da72b927c" target="[object Object]">Diagonalization and Powers of A</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/dc7fc70b89cb4fc9adbcd592a1c205f0" target="[object Object]">Diagonalization and Powers of A (00:51:50)</a></td>
<td><a href="/assets/courseware/v1/3a9097c7342f1022aa9e3395196125eb/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.9_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/a504def83cf04878bfba2303e179111f " target="[object Object]">Powers of a Matrix (00:09:06)</a></td>
<td>
<p><a href="/assets/courseware/v1/10d5af51726dae1d8666ca22481f0ec3/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.9_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/dba94848a627656c7cf4a565046bffd6/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.9_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/189fbd5bc485431b8c222616bda17e3b" target="[object Object]">Differential Equations and exp(At)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/f392a0c081c24342a0d6bfa3df37288a" target="[object Object]">Differential Equations and exp(At) (00:51:03)</a></td>
<td><a href="/assets/courseware/v1/7e8cc08351145a742866ee78c64ce222/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.0_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/3cd31de824254c70974d3650a1d811df" target="[object Object]">Differential Equations and exp(At) (00:10:19)</a></p>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/178439ff68ab4513a8d1a7f8ee8ec506 " target="[object Object]">微分方程指数矩阵(At) (00:14:36)</a></p>
</td>
<td>
<p><a href="/assets/courseware/v1/5191b9fd9b8252001d41dd65cc8b177b/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.0_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/52a3f2b171a41a2c26ef6cc11c50962c/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.0_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b9726932d9f74a17b9a12e3197fd23f5 " target="[object Object]">Markov Matrices; Fourier Series</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/bb714e9a83a649b482bf52c5c4aa34ff" target="[object Object]">Markov Matrices; Fourier Series (00:51:12)</a></td>
<td><a href="/assets/courseware/v1/ac06e8037bb5301e8969690038175542/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.1_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/914282ee5f984fadb41d050d63fb797b" target="[object Object]">Markov Matrices (00:11:48)</a></td>
<td>
<p><a href="/assets/courseware/v1/ad70b64c0cb12b8f0c93ce380e1aefe3/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.1_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/53e74e32be3528bdcb577a7c5db8dd76/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.1_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4cd1c8ffacaf49d29dcbea92b27f4ff4" target="[object Object]">Exam 2 Review</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/33dbbf60718145cda26af6f512fcb0d8" target="[object Object]">Exam 2 Review (00:48:20)</a></td>
<td><a href="/assets/courseware/v1/178872c18e7b215653b50dfe97f63494/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.02_Unit_II_3.2_LecSum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/15bd92c63aba405aa8300fb6d8df2496" target="[object Object]">Exam 2 Problem Solving (00:17:51)</a></p>
<p><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/71f8f27b47434d3c9bba95628b4d1fb5" target="[object Object]">第二次考试例题 (00:18:36)</a></p>
</td>
<td>None</td>
</tr>
</tbody>
</table>
<h2>Exam 2</h2>
<table>
<thead>
<tr><th scope="col">EXAM</th><th scope="col">EXAMS AND SOLUTIONS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/0306520e6ec94892ad97de103ce18a63" target="[object Object]">Exam 2</a></td>
<td>
<p><a href="/assets/courseware/v1/565c749630541cd393ed1d7494173670/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.3_Exam.pdf" target="[object Object]">Exam (PDF)</a></p>
<p><a href="/assets/courseware/v1/b4186bd25a77bf613defce9b68b5b0e7/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_3.3_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
</tbody>
</table>
<h2>Unit III: Positive Definite Matrices and Applications</h2>
<table>
<thead>
<tr><th scope="col">TITLES</th><th scope="col">LECTURE VIDEOS</th><th scope="col">LECTURE NOTES</th><th scope="col">PROBLEM SOLVING VIDEOS</th><th scope="col">PROBLEM SETS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/7bf69da5a7dc43a0b9c11ff7ae09e994" target="[object Object]">Symmetric Matrices and Positive Definiteness</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/bf2bb4c08d3d4868b07ad33efbe7ec71" target="[object Object]">Symmetric Matrices and Positive Definiteness (00:43:52)</a></td>
<td><a href="/assets/courseware/v1/cab5499c222e68da66e3c4ad960fa901/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.1_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/8d143859f7574aaba45e9f0c6cc58f4d" target="[object Object]">Symmetric Matrices and Positive Definiteness (00:13:05)</a></td>
<td>
<p><a href="/assets/courseware/v1/8eaac6bd6834d8037930f84cbd47a148/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.1_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/844fe7395cda1717cf2ccc77c566f8c2/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.1_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b2db393c4abc42059f95443ca3bf77d3" target="[object Object]">Complex Matrices; Fast Fourier Transform (FFT)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/7cc8a84bcdcc46d79ab0128cb25aca6f" target="[object Object]">Complex Matrices; Fast Fourier Transform (FFT) (00:47:52)</a> </td>
<td><a href="/assets/courseware/v1/e9bdec8f9218a4c608e22ffc81071f64/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.2_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/71ac99e56dfb47cb819948e3fdb00e1c" target="[object Object]">Complex Matrices (00:13:00)</a> </td>
<td>
<p><a href="/assets/courseware/v1/39417b96cf535a4b742dd36aea5ae341/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.2_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/bc11070447dfc5a773d518ba1d9c477f/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.2_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c20d83eaac7f4cc191ee7b4933ad4acd" target="[object Object]">Positive Definite Matrices and Minima</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/6362c49829ae4e5ebe8bc7820e93de9b" target="[object Object]">Positive Definite Matrices and Minima (00:50:40)</a></td>
<td><a href="/assets/courseware/v1/acff24273b14a03888da87bf4e2d2a49/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.3_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b2227788ee954552b53a74b196b43563" target="[object Object]">Positive Definite Matrices and Minima (00:12:49)</a></td>
<td>
<p><a href="/assets/courseware/v1/bb6fc08a9d2f61ac2d904e1c4c77f7ab/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.3_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/16ff8c35af674d4b3590a285f0da232a/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.3_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4e453dfa5b934266859d53be74a8c5f1" target="[object Object]">Similar Matrices and Jordan Form</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/b37ae8f85e7e4f69859c4f7f3a0c76cd" target="[object Object]">Similar Matrices and Jordan Form (00:45:56)</a></td>
<td><a href="/assets/courseware/v1/1d4a43bc7ca20ae9e994144535fed4a0/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ecb86f9d8e1148fd909d371c9d356bcb" target="[object Object]">Similar Matrices (00:08:12)</a></td>
<td>
<p><a href="/assets/courseware/v1/d399865e39920cb62b7ea554223b111e/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/789956d68d1adb808538dac68d6f40e6/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/6856f4ef27b44f77bf3d32f972080a19" target="[object Object]">Singular Value Decomposition</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/cb902694237947239a95c6809c33f930 " target="[object Object]">Singular Value Decomposition (00:41:35)</a></td>
<td><a href="/assets/courseware/v1/8e3a798414382ce594612992f23939a5/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_5_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/24dea014bcb542a6aff364e5bde79e66" target="[object Object]">Computing the Singular Value Decomposition (00:11:35)</a></td>
<td>
<p><a href="/assets/courseware/v1/14bf552efaad5bb332953e144ac6ef75/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_5_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/961dbe18ea223bfdb6d403b98652bd45/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_5_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/91ca10babbfa43489178e96e1bba077f" target="[object Object]">Linear Transformations and their Matrices</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4e3e3cb251704d8396406be700831982" target="[object Object]">Linear Transformations and their Matrices (00:49:27)</a></td>
<td><a href="/assets/courseware/v1/4eb7edf6ce7197d08937a9cbb221266a/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_6_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/ce753d6bd3504849bf156559190e1dbb" target="[object Object]">Linear Transformations (00:10:46)</a></td>
<td>
<p><a href="/assets/courseware/v1/bdd3b11f6b410917db86f83509e17bf6/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_6_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/0b98cdb869ba075520e618449fe2cd70/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_6_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/17736fa4159746a6b31d63d370ad4748" target="[object Object]">Change of Basis; Image Compression</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/26e1ae77a3d64aed88ebea73e4b9c959" target="[object Object]">Change of Basis; Image Compression (00:50:14)</a></td>
<td><a href="/assets/courseware/v1/0b6db0a2cd4452e2f613d98a9daabf10/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.7_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/290b3b5c50744ea69c63320de9d86cc7 " target="[object Object]">Change of Basis (00:12:25)</a></td>
<td>
<p><a href="/assets/courseware/v1/12d3cfdcdcf2f4b65ddcf6a56d7f6d3e/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.7_Exercises.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/cbb6afbc2806419285287b2ba2dbfcc3/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.7_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c693c49a611e460aa0792943b6ce938d" target="[object Object]">Left and Right Inverses; Pseudoinverse</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/7a0fac69e9a845eab743baa9eb7b5b57" target="[object Object]">Left and Right Inverses; Pseudoinverse (00:41:53)</a></td>
<td><a href="/assets/courseware/v1/a5eef512d536b541f9983e7e9025b1f1/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.8_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c6b28fefff1f46768d0b3a44d9ca01cc" target="[object Object]">Pseudoinverses (00:14:39)</a></td>
<td>
<p><a href="/assets/courseware/v1/55349fce11cf26775132a0c890ba9e59/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.8_Problems.pdf" target="[object Object]">Problems (PDF)</a></p>
<p><a href="/assets/courseware/v1/595d92a31dd90a2f9fd932d1c8a01468/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3.8_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/c677317200e1497d804775da24884fca" target="[object Object]">Exam 3 Review</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/74f76cd2f0854804b8f24d893d861f85" target="[object Object]">Exam 3 Review (00:47:06)</a></td>
<td><a href="/assets/courseware/v1/28ee70a771bff5cc3c8f15ff105ba95d/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_Exam_3_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/4227341269ee4929b3c287e3e5dc510f " target="[object Object]">Exam 3 Problem Solving (00:12:49)</a></td>
<td>None</td>
</tr>
</tbody>
</table>
<h2>Exam 3</h2>
<table>
<thead>
<tr><th scope="col">EXAM</th><th scope="col">EXAMS AND SOLUTIONS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/248b9a8361a84606822f8ab4a7739454" target="[object Object]">Exam 3</a></td>
<td>
<p><a href="/assets/courseware/v1/b9ee2babece78627ffd3cd79be54fd50/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_Exam.pdf" target="[object Object]">Exam (PDF)</a></p>
<p><a href="/assets/courseware/v1/3abb82e9efb132f4c13144174153a06b/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_Exam_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
</tbody>
</table>
<h2>Final Course Review</h2>
<table>
<thead>
<tr><th scope="col">TITLES</th><th scope="col">LECTURE VIDEOS</th><th scope="col">LECTURE NOTES</th><th scope="col">PROBLEM SOLVING VIDEOS</th><th scope="col">PROBLEM SETS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/0d5efa65c5634f0bacc98f1cbce1b691" target="[object Object]">Final Course Review</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/5d84d724cb95441f9a1e447dc6e89886" target="[object Object]">Final Course Review (00:43:25)</a></td>
<td><a href="/assets/courseware/v1/14edff15d626482a3356d7ca9a8469fa/asset-v1:OCW+18.06SC+2T2019+type@asset+block/Final_Course_Review_Lecsum.pdf" target="[object Object]">Lecture summary (PDF)</a></td>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/90d52cb84681469f97e3fc54fbd386a7" target="[object Object]">Final Exam Problem Solving (00:12:16)</a></td>
<td>None</td>
</tr>
</tbody>
</table>
<h2>Final Exam</h2>
<table>
<thead>
<tr><th scope="col">FINAL EXAM</th><th scope="col">EXAMS AND SOLUTIONS</th></tr>
</thead>
<tbody>
<tr>
<td><a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/9bebad1708354dda80de2d8087c8240b" target="[object Object]">Final Exam</a></td>
<td>
<p><a href="/assets/courseware/v1/a18c22a69a160608322a1cf07c60d295/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Final_Exam.pdf" target="[object Object]">Exam (PDF)</a></p>
<p><a href="/assets/courseware/v1/eae8b57e761c2a0de5a2c7bea4c49877/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Final_Exam_Solutions.pdf" target="[object Object]">Solutions (PDF)</a></p>
</td>
</tr>
</tbody>
</table>
<p></p>
</div>
</div>
</div>
</div>