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: 25

Answer

$det(A)=4x-2y-2$

Work Step by Step

$ \begin{bmatrix} x & y & 1 \\ 2& 3 & 1 \\ 0 & -1 & 1 \end{bmatrix} $ $M_{11}= \begin{bmatrix} 3 &1 \\ -1& 1\\ \end{bmatrix} = 3\times1-(-1)\times1=4$ $M_{12}= \begin{bmatrix} 2 &1\\ 0& 1\\ \end{bmatrix}=2\times1-0\times1=2$ $M_{13}= \begin{bmatrix} 2 &3 \\ 0& -1\\ \end{bmatrix}= 2(-1)-0\times3=-2$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=4$ $C_{12}=-2$ $C_{13}=-2$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=x\times4+y\times(-2)+1\times(-2)$ $det(A)=4x-2y-2$
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