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Unformatted text preview: A ) ⊥ = n-2, and (Im A ) ⊥ = ker A T . Since dim(ker A T ) + dim(Im A T ) = n , you get dim (Im A T ) = 2. This is an example of what follows from row rank equals column rank: the column rank of A is the dimension of Im(A), and the row rank is the dimension of Im( A T ). So row rank equals column rank implies that the dimensions of images are equal. [This is also Bretscher Theorem 5.3.9(c).]...
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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