solutions_501_06

solutions_501_06 - §O(v]/CC\S MATH 323-501, QUIZ 6. Fall...

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Unformatted text preview: §O(v]/CC\S MATH 323-501, QUIZ 6. Fall 2010 NAME..______"______~_._ ROW ________ _- Show all steps for credit. Q1. (4 pts.) Find bases for the row and column spaces of the matrix I - ( L 3 a " O I l ’1) 0 l ‘ , x y 'Z(, O ( ( 0 0 0 .— X (KM/A): NZC) 0o Q2. (3 pts.) For the bases B = {(170117 (1,2)T}7 C = {(1,2)T7 (1,3)T} in R2, find the transition matrix from B to C. ,x a 1') UEK,(( Z> Mgr-C (1 3 Q3. (3 pts) Let A, and Bbe nxn matrices with B invertible, and let C’ 2 BA. Prove that a vector x E R" satisfies Ax = 0 if and only if Ca: 2 0, and prove that A and C have the same rank. lag Ay:O(:e\% @Ak>gO?—CD. \L gkkgo Lka—x gvéA’krAD 04’ AX’Z—O. 6L¢ m6: 35M £44k» w“ __..T.~____~__‘iuh_-__.___ww_w_wi,H,‘ WM A mu U “MAT A mm 4A.. H ...
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solutions_501_06 - §O(v]/CC\S MATH 323-501, QUIZ 6. Fall...

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