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: 21

Answer

$det(A)=-30$

Work Step by Step

$ \begin{bmatrix} 2 & 4 & 6 \\ 0& 3 & 1 \\ 0 & 0 & -5 \end{bmatrix} $ $M_{11}= \begin{bmatrix} 3 &1 \\ 0& -5\\ \end{bmatrix} = 3\times5-0(1)=-15$ $M_{12}= \begin{bmatrix} 0 &1 \\ 0& -5\\ \end{bmatrix}=0\times(-5)-0\times1=0$ $M_{13}= \begin{bmatrix} 0 &3 \\ 0& 0\\ \end{bmatrix}= 0\times0-0\times3=0$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=-15$ $C_{12}=0$ $C_{13}=0$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=2\times(-15)+4(0)+6(0)$ $det(A)=-30$
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