M 340L HW 8 Solutions

Explanation after expanding by co factors along the

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Unformatted text preview: 3 B = a11 a12 a13 a31 a32 a33 is obtained from a11 A = b1 a31 a12 b2 a32 a13 b3 a33 by interchanging rows 1 and 2, then det[B ] = − det[A] . Explanation: After expanding by co-factors along the first row in B , we see that a12 a32 det[B ] = b1 det − b2 det a11 a31 a13 a33 a a13 + b3 det 11 a31 a33 a12 . a32 On the other hand, after expanding by cofactors along the second row in A, we see that det[A] = −b1 det + b2 det a11 a31 a12 a32 a13 a33 a a13 − b3 det 11 a31 a33 Consequently, det[B ] = − det[A] . a12 . a32 4 cruz (fmc326) – HW08 – gilbert – (56540) 010 1...
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This document was uploaded on 03/16/2014 for the course M 340L at University of Texas.

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