The Null Space & Column Space of a Matrix | Algebraically & Geometrically

To every matrix, there are two natural subspaces: the Null Space of A, and the Column Space of A, denoted Null(A) and Col(A). Col(A) is the range, or all the vectors "hit" by a transformation. It turns out this is equivalent to the span of the columns of A. Null(A) is all the vectors in the domain that are sent to zero by the transformation. We visualize these two subspaces, prove they actually are subspaces, and show how to compute them.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.

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Видео The Null Space & Column Space of a Matrix | Algebraically & Geometrically канала Dr. Trefor Bazett