Unformatted text preview: A T ? Solution: The dimension of (ker A ) ⊥ = m2, and (ker A ) ⊥ = Im A T . Since dim(ker A T ) + dim(Im A T ) = n , you get dim (ker A T ) = nm + 2. There is a puzzle here: why can’t nm+2 be negative? The answer is that, if the kernel of A has dimension 2, then the image of A has dimension m2, and that is a subspace of R n . So you must have n ≥ m2....
View
Full
Document
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
 lee
 Vectors

Click to edit the document details