Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 3 - Determinants - 3.1 The Determination of a Matrix - 3.1 Exercises: 19

Answer

$det(A)=-58$

Work Step by Step

$ \begin{bmatrix} 1 & 4 & -2 \\ 3 & 2 & 0 \\ -1 & 4 & 3 \end{bmatrix} $ $M_{11}= \begin{bmatrix} 2 &0 \\ 4& 3\\ \end{bmatrix} = 2\times3-4(0)=6$ $M_{12}= \begin{bmatrix} 3 &0 \\ -1& 3\\ \end{bmatrix}=3\times3-(-1)0=9$ $M_{13}= \begin{bmatrix} 3 &2 \\ -1& 4\\ \end{bmatrix}= 3\times4-(-1)2=14$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=6$ $C_{12}=-9$ $C_{13}=14$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=1\times6+4\times(-9)-2\times14$ $det(A)=-58$
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