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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.
 Spring '08
 PAVLOVIC
 Matrices

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