<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@15b479b3f3384243a1eb1d5d62ab4ad7" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<h2 class="hd hd-2 unit-title">2.3 Session Overview</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@416cde6c7ef2425cbb7085f5cfce8c90">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@416cde6c7ef2425cbb7085f5cfce8c90" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<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/v1/8ccc8a7c048b71c7a1ea03a23c809aab/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_Session_Overview.jpg" alt="Figured excerpted from 'Introduction to Linear Algebra' by G.S. Strang" /></div>
<p>This session explores the linear algebra of electrical networks and the Internet, and sheds light on important results in graph theory.</p>
<p></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@45113d95de654c93aafb804db64fff76" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<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@34b54b075df2431b93b8ee741cd05e2c">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@video+block@34b54b075df2431b93b8ee741cd05e2c" data-runtime-class="LmsRuntime" data-block-type="video" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Graphs, Networks, Incidence Matrices</h3>
<div
id="video_34b54b075df2431b93b8ee741cd05e2c"
class="video closed"
data-metadata='{"speed": null, "saveStateEnabled": false, "streams": "1.00:6-wh6yvk6uc", "savedVideoPosition": 0.0, "ytTestTimeout": 1500, "generalSpeed": 1.0, "poster": null, "publishCompletionUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@34b54b075df2431b93b8ee741cd05e2c/handler/publish_completion", "completionEnabled": false, "autoplay": false, "completionPercentage": 0.95, "captionDataDir": null, "duration": 0.0, "saveStateUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@34b54b075df2431b93b8ee741cd05e2c/handler/xmodule_handler/save_user_state", "ytApiUrl": "https://www.youtube.com/iframe_api", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "prioritizeHls": false, "autoAdvance": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@34b54b075df2431b93b8ee741cd05e2c/handler/transcript/translation/__lang__", "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@34b54b075df2431b93b8ee741cd05e2c/handler/transcript/available_translations", "ytMetadataEndpoint": "", "recordedYoutubeIsAvailable": true, "sources": ["https://archive.org/download/MIT18.06S05_MP4/12.mp4"], "showCaptions": "true", "end": 0.0}'
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="34b54b075df2431b93b8ee741cd05e2c"></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_34b54b075df2431b93b8ee741cd05e2c">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_34b54b075df2431b93b8ee741cd05e2c">
<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_MP4/12.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@34b54b075df2431b93b8ee741cd05e2c/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@34b54b075df2431b93b8ee741cd05e2c/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@e435877d34664d8eadb2992101bb6b35">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@e435877d34664d8eadb2992101bb6b35" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><a href="/assets/courseware/v1/0d6ba9804a27201f4310f20753f0c43a/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_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-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@3007c8a8a5ca4f1cb08ec17e9bb3c3bd" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<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@c11bd517f7a14ee399b57be6c8dc5769">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@c11bd517f7a14ee399b57be6c8dc5769" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<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/b448f54b965be71a70d6bb2e9bd6e4b7/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_LecSum.pdf" target="[object Object]">Graphs, Networks, Incidence Matrices (PDF)</a></li>
</ul>
<h3>Suggested Reading</h3>
<ul>
<li>Read Section 8.2 in the 4<sup>th</sup> edition or Section 10.1 in the 5<sup>th</sup> edition.</li>
</ul>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@c1fae46167ef470695015c5df649c4fc" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<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@ae06545f4b9c4611afe55bc7e7cb75d6">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@video+block@ae06545f4b9c4611afe55bc7e7cb75d6" data-runtime-class="LmsRuntime" data-block-type="video" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Graphs and Networks</h3>
<div
id="video_ae06545f4b9c4611afe55bc7e7cb75d6"
class="video closed"
data-metadata='{"speed": null, "saveStateEnabled": false, "streams": "1.00:h0m2tsmSPTI", "savedVideoPosition": 0.0, "ytTestTimeout": 1500, "generalSpeed": 1.0, "poster": null, "publishCompletionUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@ae06545f4b9c4611afe55bc7e7cb75d6/handler/publish_completion", "completionEnabled": false, "autoplay": false, "completionPercentage": 0.95, "captionDataDir": null, "duration": 0.0, "saveStateUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@ae06545f4b9c4611afe55bc7e7cb75d6/handler/xmodule_handler/save_user_state", "ytApiUrl": "https://www.youtube.com/iframe_api", "start": 0.0, "transcriptLanguage": "en", "lmsRootURL": "https://openlearninglibrary.mit.edu", "prioritizeHls": false, "autoAdvance": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@ae06545f4b9c4611afe55bc7e7cb75d6/handler/transcript/translation/__lang__", "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@ae06545f4b9c4611afe55bc7e7cb75d6/handler/transcript/available_translations", "ytMetadataEndpoint": "", "recordedYoutubeIsAvailable": true, "sources": ["https://archive.org/download/MIT18.06SCF11/MIT18_06SC_110711_N1_300k.mp4"], "showCaptions": "true", "end": 0.0}'
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="ae06545f4b9c4611afe55bc7e7cb75d6"></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_ae06545f4b9c4611afe55bc7e7cb75d6">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_ae06545f4b9c4611afe55bc7e7cb75d6">
<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_110711_N1_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@ae06545f4b9c4611afe55bc7e7cb75d6/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@ae06545f4b9c4611afe55bc7e7cb75d6/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@51ce5b061f1641a3a51c76f13c22649c">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@51ce5b061f1641a3a51c76f13c22649c" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><a href="/assets/courseware/v1/c9db52781471990c70a1626bdf6e578d/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_2.3_RecitationTrans.pdf" target="[object Object]">Recitation video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-init="VerticalStudentView" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@433de512faa44d499ca25ca22d722c84" data-runtime-class="LmsRuntime" data-block-type="vertical" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<h2 class="hd hd-2 unit-title">Problems and Solutions</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@b2f408090bbb463c957bd4e13d47db93">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-init="XBlockToXModuleShim" data-has-score="False" data-runtime-version="1" data-graded="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@b2f408090bbb463c957bd4e13d47db93" data-runtime-class="LmsRuntime" data-block-type="html" data-request-token="b597a19e035b11efb61b02329aca76dd" data-course-id="course-v1:OCW+18.06SC+2T2019">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>Work the problems on your own and check your answers when you're done.</p>
<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]">Exercises on graphs, networks, and incidence matrices (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 to graphs, networks, and incidence matrices (PDF)</a></p>
</div>
</div>
</div>
</div>