Quiz3 solutions 225 - Math 225 Quiz 3 Use both sides of the...

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Unformatted text preview: September 17, 2009 Math. 225 - Quiz 3 Use both sides of the paper if necessary (1) Let A = 3 1 2 0 . and b = 8 −2 3 7 (a) Re-write the matrix equation AX = b as a vector equation. [Hint: use the columns of A]. 1 3 (b) Given that X = 1 and X ′ = 0 are both solutions to the AX = b, 1 2 without doing any row reduction or elimination, write down a solution to the homogeneous equation AX = 0. 2 3 0 , and C = 2. (2) Let A = 1 2 −1 , B = −3 3 (a) compute both AB and BA. (b) Compute, or say why it can’t be done: A + B, A + C, B + C Solutions (1a) x1 1 2 0 3 + x2 + x3 = −2 3 7 8 (1b) If X and X ′ are solutions to Ax = b then A(X − X ′ ) = 0, i.e. the solution asked for is −2 X − X′ = 0 −1 (2a) AB = 2 + 0 + 3 = 5 , 2 4 −1 0 0 BA = 0 −3 −6 3 (2b) Addition is defined only for matrices of the same shape. Since A is a 3 × 1 matrix but B and C are 1 × 3 matrices it follows that only B + C is defined. 2+3 5 0 + 2 = 2 B+C = −3 + 3 0 ...
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This note was uploaded on 09/01/2010 for the course MATH math 225 taught by Professor Bradlow during the Fall '09 term at University of Illinois at Urbana–Champaign.

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Quiz3 solutions 225 - Math 225 Quiz 3 Use both sides of the...

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