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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 = 1 1 1 2 1 2 0 - 1 B = 1 - 1 1 2 1 0 4 - 1 2 C = 2 1 0 2 1 - 2 5 1 D = 0 1 1 0 v = 1 1 x = 1 - 1 y = 2 - 1 2 z = - 1 - 1 3 2 SOLUTION A z = 5 - 5 B y = 5 3 13 C v = 3 2 - 1 6 C x = 1 - 2 3 4 D v = 1 1 D x = - 1 1 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
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