1. Let A and B be matrices of relevant dimensions, and AB = 0. Can we say that the columns of B are in the nullspace of A? What about the columns of A? Justify your answer mathematically. 2. Show that the nullspace of AT A is also the nullspace of A.

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orthogonality of subspaces and projections
1. Let A and B be matrices of relevant dimensions, and AB = 0. Can we say
that the columns of B are in the nullspace of A? What about the columns of
A? Justify your answer mathematically.
2. Show that the nullspace of AT A is also the nullspace of A.
Transcribed Image Text:orthogonality of subspaces and projections 1. Let A and B be matrices of relevant dimensions, and AB = 0. Can we say that the columns of B are in the nullspace of A? What about the columns of A? Justify your answer mathematically. 2. Show that the nullspace of AT A is also the nullspace of A.
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