Linear Algebra Example Problems - Subspace Dimension #2 (Rank Theorem)

The last few videos on the play list have examined the null space, column space, and row space of a matrix. We found the dimension of each of these subspaces by explicitly constructing a basis and then counting the number of basis vectors to determine the subspace dimension.

The Rank Theorem quantifies the relationships between various subspace dimensions of a matrix. For example, the column space and row space must always have the same dimension which is referred to as the "rank" of a matrix. Also, the rank of an mxn matrix and the dimension of its null space must always sum to n.

[jonasoliveira]

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[klelusive]

Thank you for the very easy to understand explanations

[randomideas]

can't thank you enough. i was looking for such example. bundle of good wishes

[ganghyeonkim]

so would the nullity of B = 4? since n is now 6 and rank(B) = 2?