09_hwc1SolnsODDA

09_hwc1SolnsODDA - 2.7 Consider the following list of 4...

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2.7 Consider the following list of 4 matrices and 4 vectors. There are 16 different pairs of matrices and vectors. Say for which pairs the matrix–vector product is defined, for which it isn’t, and compute it when it is. A = h 1 1 1 2 1 2 0 - 1 i B = ± 1 - 1 1 2 1 0 4 - 1 2 ² C = 2 1 0 2 1 - 2 5 1 D = h 0 1 1 0 i v = h 1 1 i x = h 1 - 1 i y = ± 2 - 1 2 ² z = - 1 - 1 3 2 SOLUTION A z = ± 5 - 5 ² B y = 5 3 13 C v = 3 2 - 1 6 C x = 1 - 2 3 4 D v = ± 1 1 ² D x = ± - 1 1 ² 2.9 Let A = 1 1 1 2 1 2 0 - 1 2 0 0 - 1 3 - 2 0 2 and x = - 1 - 2 2 1 . Compute the third entry of A x without computing the whole vector A x . SOLUTION Using Theorem 3, ( A x ) 3 = - 1(2) - 2(0) + 2(0) + 1( - 1) = - 3 . 2.11 Let f be a linear transformation from IR 2 to IR 2
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.

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