sol-assignment4 - A and 1 B be in M nn det(A = det(B =0...

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1 University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear algebra II MATB24 Fall 2010 Section 3.3
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4 Section 3.4
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5 3. Addition: 1) Yes. p(x), q(x) P n , T[p(x)] = p(0) and T[q(x)] = q(0). T[(p + q)(x)] = (p + q)(0) = p(0) + q(0) = T[p(x)] + T[q(x)] T[(rp)(x)] = (rp)(0) = rp(0). 2) No. Let 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
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Unformatted text preview: A and 1 B be in M nn . det(A) = det(B) =0 det(A + B) = det(I) = 1 3) No. T( 0 ) = 0 + u The T desn’t preserve zero vector. 4) Yes. The proof is similar to 1)....
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sol-assignment4 - A and 1 B be in M nn det(A = det(B =0...

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