Linear Algebra 451 The Dimension of a Vector Space

>> DOWNLOAD LINK 🎞️ #1 <<

>> DOWNLOAD LINK 🎞️ #2 <<

>> COPY / PASTE LINK PLEASE 🎵 MP3 <<

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=jk6YPdIIJUg

An introduction to finding the dimension of a vector space","styleRuns":[{"startIndex":0,"length":58,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":58,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"COMBELsvGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC2prNllQZElJSlVnGAYyJSIRIgtqazZZUGRJSUpVZzAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"COMBELsvGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"COIBELovIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"lgKR0iJi7Ww","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/lgKR0iJi7Ww/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBAf1grVBi6wTpeiNf55NBT__Skmw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/lgKR0iJi7Ww/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAYAlwfAxV3c35hD8ba9QKAtLTrQA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Linear Algebra 4.5.2 Subspaces of a Finite Dimensional Space by Kimberly Brehm 40,535 views 5 years ago 9 minutes, 49 seconds"}},"simpleText":"Linear Algebra 4.5.2 Subspaces of a Finite Dimensional Space"},"longBylineText":{"runs":[{"text":"Kimberly Brehm","navigationEndpoint":{"clickTrackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SawFinMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCcbu9qaBn3MNFYr96mbg72w","canonicalBaseUrl":"/@SawFinMath"}}}]},"publishedTimeText":{"simpleText":"5 years ago"},"viewCountText":{"simpleText":"40,535 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 49 seconds"}},"simpleText":"9:49"},"navigationEndpoint":{"clickTrackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWRIyMqgkN2HpqeOAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=lgKR0iJi7Ww","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"lgKR0iJi7Ww","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=960291d22262ed6c ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=836250 mt=1740005341 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Kimberly Brehm","navigationEndpoint":{"clickTrackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SawFinMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCcbu9qaBn3MNFYr96mbg72w","canonicalBaseUrl":"/@SawFinMath"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/Ty-cJztjB4F7voHKTRaSRMX_walOg1L5ZAzTBZSlmIiBGeVqWa8VkQs3eXn6LY7kP-oASCn_KQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpxA7NqLk6K6pIGWAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"40K views"}},"simpleText":"40K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"COABEP6YBBgFIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"COABEP6YBBgFIhMI6Iyju-rQiwMV-2B6BR06XAqc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"lgKR0iJi7Ww","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"COABEP6YBBgFIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["lgKR0iJi7Ww"],"params":"CAQ%3D"}},"videoIds":["lgKR0iJi7Ww"]}},{"clickTrackingParams":"COABEP6YBBgFIhMI6Iyju-rQiwMV-2B6BR06XAqc","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"COEBELlqIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},"popupType":"TOAST"}}]}},"trackingParams":"COABEP6YBBgFIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CN8BENGqBRgGIhMI6Iyju-rQiwMV-2B6BR06XAqc","offlineVideoEndpoint":{"videoId":"lgKR0iJi7Ww","onAddCommand":{"clickTrackingParams":"CN8BENGqBRgGIhMI6Iyju-rQiwMV-2B6BR06XAqc","getDownloadActionCommand":{"videoId":"lgKR0iJi7Ww","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CN8BENGqBRgGIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtsZ0tSMGlKaTdXdw%3D%3D","commands":[{"clickTrackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpw=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CN4BEI5iIhMI6Iyju-rQiwMV-2B6BR06XAqc","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpw=","hasSeparator":true}}],"trackingParams":"CNsBEKQwGAAiEwjojKO76tCLAxX7YHoFHTpcCpw=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 49 seconds"}},"simpleText":"9:49"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CN0BEPnnAxgBIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"lgKR0iJi7Ww","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CN0BEPnnAxgBIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"lgKR0iJi7Ww"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CN0BEPnnAxgBIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNwBEMfsBBgCIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNwBEMfsBBgCIhMI6Iyju-rQiwMV-2B6BR06XAqc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"lgKR0iJi7Ww","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNwBEMfsBBgCIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["lgKR0iJi7Ww"],"params":"CAQ%3D"}},"videoIds":["lgKR0iJi7Ww"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNwBEMfsBBgCIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Linear Algebra 4.5.2 Subspaces of a Finite Dimensional Space - 9 minutes, 49 seconds - Go to channel - Kimberly Brehm - 40K views - 5 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"dqMFVuwLa7A","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/dqMFVuwLa7A/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDyf56n6emjJkwz8HTZS6a8rV17jg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/dqMFVuwLa7A/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDQZ48NCze35lgX21apEcErUxhNqw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Vector Space by Prime Newtons 114,787 views 1 year ago 18 minutes"}},"simpleText":"Vector Space"},"longBylineText":{"runs":[{"text":"Prime Newtons","navigationEndpoint":{"clickTrackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PrimeNewtons","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQ3jbVA0UCuBJfqTWxOb1aQ","canonicalBaseUrl":"/@PrimeNewtons"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"114,787 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"18 minutes, 4 seconds"}},"simpleText":"18:04"},"navigationEndpoint":{"clickTrackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWRIyMqgkN2HpqeOAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=dqMFVuwLa7A","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"dqMFVuwLa7A","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=76a30556ec0b6bb0 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=836250 mt=1740005341 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Prime Newtons","navigationEndpoint":{"clickTrackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PrimeNewtons","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQ3jbVA0UCuBJfqTWxOb1aQ","canonicalBaseUrl":"/@PrimeNewtons"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/wxfmE3GxAAG8F4wC1QF7V5Ob9xo4MXGGnn0V-c5WeVtVFe7RrCf68SCsQT8cMPhw6sgPYbmDiqs=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpw=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpxAsNet4O6qwdF2","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"114K views"}},"simpleText":"114K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CNkBEP6YBBgHIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNkBEP6YBBgHIhMI6Iyju-rQiwMV-2B6BR06XAqc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"dqMFVuwLa7A","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNkBEP6YBBgHIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["dqMFVuwLa7A"],"params":"CAQ%3D"}},"videoIds":["dqMFVuwLa7A"]}},{"clickTrackingParams":"CNkBEP6YBBgHIhMI6Iyju-rQiwMV-2B6BR06XAqc","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNoBELlqIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},"popupType":"TOAST"}}]}},"trackingParams":"CNkBEP6YBBgHIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CNgBENGqBRgIIhMI6Iyju-rQiwMV-2B6BR06XAqc","offlineVideoEndpoint":{"videoId":"dqMFVuwLa7A","onAddCommand":{"clickTrackingParams":"CNgBENGqBRgIIhMI6Iyju-rQiwMV-2B6BR06XAqc","getDownloadActionCommand":{"videoId":"dqMFVuwLa7A","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CNgBENGqBRgIIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtkcU1GVnV3TGE3QQ%3D%3D","commands":[{"clickTrackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpw=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CNcBEI5iIhMI6Iyju-rQiwMV-2B6BR06XAqc","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpw=","hasSeparator":true}}],"trackingParams":"CNQBEKQwGAEiEwjojKO76tCLAxX7YHoFHTpcCpw=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"18 minutes, 4 seconds"}},"simpleText":"18:04"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNYBEPnnAxgCIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"dqMFVuwLa7A","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CNYBEPnnAxgCIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"dqMFVuwLa7A"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNYBEPnnAxgCIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNUBEMfsBBgDIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNUBEMfsBBgDIhMI6Iyju-rQiwMV-2B6BR06XAqc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"dqMFVuwLa7A","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNUBEMfsBBgDIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["dqMFVuwLa7A"],"params":"CAQ%3D"}},"videoIds":["dqMFVuwLa7A"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNUBEMfsBBgDIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Vector Space - 18 minutes - Go to channel - Prime Newtons - 114K views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/dqMFVuwLa7A/mqdefault_6s.webp?du=3000 sqp=CPCw2b0G rs=AOn4CLD5JCoDAw_GvkY1_1wkpWqfYsxDJQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"zntNi3-ybfQ","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/zntNi3-ybfQ/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLC65HaDrzZhQ7K-gPEa209Jr50fbw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/zntNi3-ybfQ/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCU4UF9vjXxnC5S2tsVmEWG0paTMA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy by Khan Academy 1,171,655 views 15 years ago 19 minutes"}},"simpleText":"Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy"},"longBylineText":{"runs":[{"text":"Khan Academy","navigationEndpoint":{"clickTrackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@khanacademy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4a-Gbdw7vOaccHmFo40b9g","canonicalBaseUrl":"/@khanacademy"}}}]},"publishedTimeText":{"simpleText":"15 years ago"},"viewCountText":{"simpleText":"1,171,655 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"19 minutes"}},"simpleText":"19:00"},"navigationEndpoint":{"clickTrackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWRIyMqgkN2HpqeOAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=zntNi3-ybfQ","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"zntNi3-ybfQ","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=ce7b4d8b7fb26df4 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=836250 mt=1740005341 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Khan Academy","navigationEndpoint":{"clickTrackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpwyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@khanacademy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4a-Gbdw7vOaccHmFo40b9g","canonicalBaseUrl":"/@khanacademy"}}}]},"badges":[{"metadataBadgeRenderer":{"style":"BADGE_STYLE_TYPE_YPC","label":"Fundraiser","trackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpw="}}],"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_l3GggKOWViCBpDs9APIsK6MHB2Mu-ECo5dUEU-Vay2gg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpxA9NvJ_bex073OAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"1.1 million views"}},"simpleText":"1.1M views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CNIBEP6YBBgIIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNIBEP6YBBgIIhMI6Iyju-rQiwMV-2B6BR06XAqc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"zntNi3-ybfQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNIBEP6YBBgIIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["zntNi3-ybfQ"],"params":"CAQ%3D"}},"videoIds":["zntNi3-ybfQ"]}},{"clickTrackingParams":"CNIBEP6YBBgIIhMI6Iyju-rQiwMV-2B6BR06XAqc","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNMBELlqIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},"popupType":"TOAST"}}]}},"trackingParams":"CNIBEP6YBBgIIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CNEBENGqBRgJIhMI6Iyju-rQiwMV-2B6BR06XAqc","offlineVideoEndpoint":{"videoId":"zntNi3-ybfQ","onAddCommand":{"clickTrackingParams":"CNEBENGqBRgJIhMI6Iyju-rQiwMV-2B6BR06XAqc","getDownloadActionCommand":{"videoId":"zntNi3-ybfQ","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CNEBENGqBRgJIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt6bnROaTMteWJmUQ%3D%3D","commands":[{"clickTrackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CNABEI5iIhMI6Iyju-rQiwMV-2B6BR06XAqc","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","hasSeparator":true}}],"trackingParams":"CM0BEKQwGAIiEwjojKO76tCLAxX7YHoFHTpcCpw=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"19 minutes"}},"simpleText":"19:00"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CM8BEPnnAxgDIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"zntNi3-ybfQ","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CM8BEPnnAxgDIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"zntNi3-ybfQ"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CM8BEPnnAxgDIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CM4BEMfsBBgEIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CM4BEMfsBBgEIhMI6Iyju-rQiwMV-2B6BR06XAqc","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"zntNi3-ybfQ","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CM4BEMfsBBgEIhMI6Iyju-rQiwMV-2B6BR06XAqc","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["zntNi3-ybfQ"],"params":"CAQ%3D"}},"videoIds":["zntNi3-ybfQ"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CM4BEMfsBBgEIhMI6Iyju-rQiwMV-2B6BR06XAqc"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Basis of a subspace | Vectors and spaces | Linear Algebra | Khan Academy - 19 minutes - Go to channel - Khan Academy - 1.1M views - 15 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/zntNi3-ybfQ/mqdefault_6s.webp?du=3000 sqp=CLi32b0G rs=AOn4CLD4h-B8rdNTUbpyNgLc6ya4xaV03w","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/LHsPJ2bQX1U/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLCw96DcSAnGkbMJG5C-v4x2e5o-4w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/LHsPJ2bQX1U/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLBuoQ0U6Jl31ARP0ucMU06hCGM2tw","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"46 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Linear Algebra (OLD PLAYLIST)"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"Kimberly Brehm

#############################