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: 26

Answer

$det(A)=-7x+3y-8$

Work Step by Step

$ \begin{bmatrix} x & y & 1 \\ -2 & -2 & 1 \\ 1& 5 & 1 \end{bmatrix} $ $M_{11}= \begin{bmatrix} -2 &1 \\ 5& 1\\ \end{bmatrix} = -2\times1-5(1)=-7$ $M_{12}= \begin{bmatrix} -2&1\\ 1& 1\\ \end{bmatrix}=-2\times1-1\times1=-3$ $M_{13}= \begin{bmatrix} -2 &-2 \\ 1& 5\\ \end{bmatrix}= -2\times5-1(-2)=-8$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=-7$ $C_{12}=3$ $C_{13}=-8$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=x\times(-7)+y\times3-1\times(-8)$ $det(A)=-7x+3y-8$
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