What is a Subspace Passing Linear Algebra

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A subspace is just a collection of vectors that satisfies three special conditions. • Important theorem: All spans are subspaces! This should make sense if you consider how spans are defined; they meet all three requirements of subspaces!","styleRuns":[{"startIndex":0,"length":236,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":236,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CMcBELsvGAIiEwj0j_Syo9uLAxVXdnoFHQXpMf0=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC0pvZVZIUF9qZzQ0GAYyJSIRIgtKb2VWSFBfamc0NDAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CMcBELsvGAIiEwj0j_Syo9uLAxVXdnoFHQXpMf0=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CMYBELovIhMI9I_0sqPbiwMVV3Z6BR0F6TH9"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"au17uFyDupo","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/au17uFyDupo/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLB1Z5TAf4ZfvW6zaqTF24NYtg44pw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/au17uFyDupo/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDPYc_3zcRV0XfKFGPhRRCHSBi77w","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"What is a Basis for a Subspace? 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