<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="vertical" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@c677317200e1497d804775da24884fca">
<h2 class="hd hd-2 unit-title">Session Overview</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@baef46ea8c5e4c07995050bafe09663d">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="html" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@baef46ea8c5e4c07995050bafe09663d">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<div style="float: left; margin: 6px 20px auto 0px;"><img height="100" width="100" src="/assets/courseware/v1/774ed29be79939566845e079d8391ef3/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_Exam_3_Review.jpg" alt="Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang" /></div>
<p></p>
<p>Exam 3 covers the understanding of matrices through their eigenvalues. Elimination is history now, because it does NOT preserve eigenvalues. Notice the special types of matrices (like positive definite) and their factorizations.</p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="vertical" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@74f76cd2f0854804b8f24d893d861f85">
<h2 class="hd hd-2 unit-title">Lecture Video</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="video" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Exam 3 Review</h3>
<div
id="video_b1e903c24e15435da7ed87f518f32c7c"
class="video closed"
data-metadata='{"saveStateEnabled": false, "speed": null, "ytMetadataEndpoint": "", "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c/handler/transcript/available_translations", "captionDataDir": null, "completionEnabled": false, "poster": null, "generalSpeed": 1.0, "transcriptLanguages": {"en": "English"}, "transcriptTranslationUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c/handler/transcript/translation/__lang__", "start": 0.0, "end": 0.0, "savedVideoPosition": 0.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "saveStateUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c/handler/xmodule_handler/save_user_state", "ytApiUrl": "https://www.youtube.com/iframe_api", "autoAdvance": false, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c/handler/publish_completion", "showCaptions": "true", "autohideHtml5": false, "streams": "1.00:HgC1l_6ySkc", "prioritizeHls": false, "duration": 0.0, "transcriptLanguage": "en", "autoplay": false, "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "sources": ["https://archive.org/download/MIT18.06S05_MP4/32.mp4"]}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="b1e903c24e15435da7ed87f518f32c7c"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_b1e903c24e15435da7ed87f518f32c7c">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_b1e903c24e15435da7ed87f518f32c7c">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://archive.org/download/MIT18.06S05_MP4/32.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@b1e903c24e15435da7ed87f518f32c7c/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@b5cdff27f0d143a2bb8f13b4097f1bca">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="html" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@b5cdff27f0d143a2bb8f13b4097f1bca">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><a href="/assets/courseware/v1/a705c12872737ba63cce082571abd926/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_Exam_3_Lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="vertical" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@82b5d318c46d4976ac0ecb83bc26aeea">
<h2 class="hd hd-2 unit-title">Lecture Summary and Reading</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@f09a4c4971ec466890ed2240a4bad3bc">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="html" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@f09a4c4971ec466890ed2240a4bad3bc">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h3>Lecture Summary </h3>
<ul>
<li><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]">Exam 3 review (PDF)</a></li>
</ul>
<h3>Suggested Reading</h3>
<ul>
<li>Review Chapters 6 and 7, plus Sections 10.2 through 10.3 in the 4<sup>th</sup> edition or Review Chapters 6, 7, and 8 plus Sections 9.2 through 9.3 in the 5<sup>th</sup> edition.</li>
</ul>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="vertical" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@4227341269ee4929b3c287e3e5dc510f">
<h2 class="hd hd-2 unit-title">Recitation Video</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="video" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Exam 3 Problem Solving</h3>
<div
id="video_e5bbc68550304acf8d3917d962b4fb01"
class="video closed"
data-metadata='{"saveStateEnabled": false, "speed": null, "ytMetadataEndpoint": "", "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01/handler/transcript/available_translations", "captionDataDir": null, "completionEnabled": false, "poster": null, "generalSpeed": 1.0, "transcriptLanguages": {"en": "English"}, "transcriptTranslationUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01/handler/transcript/translation/__lang__", "start": 0.0, "end": 0.0, "savedVideoPosition": 0.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "saveStateUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01/handler/xmodule_handler/save_user_state", "ytApiUrl": "https://www.youtube.com/iframe_api", "autoAdvance": false, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01/handler/publish_completion", "showCaptions": "true", "autohideHtml5": false, "streams": "1.00:OsHY7ycgbaE", "prioritizeHls": false, "duration": 0.0, "transcriptLanguage": "en", "autoplay": false, "completionPercentage": 0.95, "recordedYoutubeIsAvailable": true, "sources": ["https://archive.org/download/MIT18.06SCF11/MIT18_06SC_110714_D2_300k.mp4"]}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="e5bbc68550304acf8d3917d962b4fb01"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_e5bbc68550304acf8d3917d962b4fb01">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_e5bbc68550304acf8d3917d962b4fb01">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://archive.org/download/MIT18.06SCF11/MIT18_06SC_110714_D2_300k.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@e5bbc68550304acf8d3917d962b4fb01/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@58de5a7dbc66458f8ad0f8499e2007e3">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-course-id="course-v1:OCW+18.06SC+2T2019" data-has-score="False" data-request-token="8e397e04682f11ef8c790e199eb5def5" data-runtime-version="1" data-block-type="html" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@58de5a7dbc66458f8ad0f8499e2007e3">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><a href="/assets/courseware/v1/f4781aa56d72317f7c2be4a75ada6ec2/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_Exam_3_Rectrans.pdf" target="[object Object]">Recitation video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>