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Unformatted text preview: or null space of A ). (b) Prove that r ( A ) < n . (c) If r ( A ) < n-1 , prove that cof i,j ( A ) = 0 for all 1 ≤ i < j ≤ n, where cof i,j A denotes the ( i, j )-cofactor of A . (d) Prove that ( cof i, 1 ( A ) , . . . , cof i,n ( A )) T ∈ ker A , for i = 1 , . . . , n. (e) Hence, or otherwise, prove that the value of cof i,j is independent of i and j....
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This note was uploaded on 05/23/2010 for the course MATH 235 taught by Professor Celmin during the Winter '08 term at Waterloo.
- Winter '08