Unformatted text preview: A has two rows, so DA is the only product with D on the left that makes sense. We now use the deﬁnition of the matrix product to compute the products identiﬁed above: AC = ± 13 33 4 ² BB = 33 3 41 2 107 8 CA = 3 4 2 3 2 4213 1 4 6 7 5 9 CD = 1 2 22 1 1 5 DA = ± 1 21 1 1 1 2 ² DD = ± 1 1 ² 3.3 Let A = 1 1 1 2 1 21 21 32 2 and let B = 1 1 1 1 1 11 2 3 133 . Compute the third column of AB by computing an appropriate matrix–vector product. SOLUTION By the deﬁnition of matrix–matrix multiplication, if we write B = [ v 1 , v 2 , v 3 , v 4 ] , then AB = [ A v 1 , A v 2 , A v 3 , A v 4 ] . Therefore, we just need to compute A v 3 , which is 3 3 2 1 . 21 /september/ 2005; 22:09 19...
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 Fall '08
 Gladue
 Calculus, Multiplication, Matrices, appropriate matrix–vector product

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