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: 20

Answer

$det(A)=2$

Work Step by Step

$ \begin{bmatrix} 2 & -1 & 3 \\ 1 & 4 & 4 \\ 1& 0 & 2 \end{bmatrix} $ $M_{11}= \begin{bmatrix} 4 &4 \\ 0& 2\\ \end{bmatrix} = 4\times2-0(4)=8$ $M_{12}= \begin{bmatrix} 1 &4 \\ 1& 2\\ \end{bmatrix}=1\times2-1\times4=-2$ $M_{13}= \begin{bmatrix} 1 &4 \\ 1& 0\\ \end{bmatrix}= 1\times0-1\times4=-4$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=8$ $C_{12}=2$ $C_{13}=-4$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=2\times8+(-1)\times2+3\times(-4)$ $det(A)=2$
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