Unformatted text preview: A T ? Solution: The dimension of (ker A ) ⊥ = m-2, and (ker A ) ⊥ = Im A T . Since dim(ker A T ) + dim(Im A T ) = n , you get dim (ker A T ) = n-m + 2. There is a puzzle here: why can’t n-m+2 be negative? The answer is that, if the kernel of A has dimension 2, then the image of A has dimension m-2, and that is a subspace of R n . So you must have n ≥ m-2....
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This note was uploaded on 02/06/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
- Fall '08