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: 22

Answer

$det(A)=-66$

Work Step by Step

$ \begin{bmatrix} -3 & 0 & 0 \\ 7 & 11 & 0 \\ 1& 2 & 2 \end{bmatrix} $ $M_{11}= \begin{bmatrix} 11 &0 \\ 2& 2\\ \end{bmatrix} = 11\times2-2\times0=22$ $M_{12}= \begin{bmatrix} 7 &0 \\ 1& 2\\ \end{bmatrix}=7\times2-1\times0=14$ $M_{13}= \begin{bmatrix} 7 &11 \\ 1& 2\\ \end{bmatrix}= 7\times2-1\times11=3$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=22$ $C_{12}=-14$ $C_{13}=3$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=-3\times22+0\times(-14)+0\times3$ $det(A)=-66$
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