M 340L HW 8 Solutions

Det b 5 2 true correct 32 correct 3 det b 5 1 false

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Unformatted text preview: 1 ka12 ka13 det a21 a22 a23 = ka11 det[A11 ] a31 a32 a33 = −10 4. det B 5 2. TRUE correct = −32 correct 3. det B 5 1. FALSE = −2 2. det B 5 2 = 32 − ka12 det[A12 ] + ka13 det[A13 ] = k (a11 det[A11 ] − a12 det[A12 ] + a13 det[A13 ]). On the other hand, Explanation: Since det[A] = a11 det[A11 ] det[CD] = det[C ] det[D] , Thus for all n × n matrices C and D, det B 5 = (det[B ])5 . But det[B ] = 1 1 1 − a12 det[A12 ] + a13 det[A13 ] . 01 12 21 ka11 a21 det a31 ka13 a23 = k det[A] , a33 ka12 a22 a32 so the row operation scaling a row also sca...
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This document was uploaded on 03/16/2014 for the course M 340L at University of Texas at Austin.

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