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: 14

Answer

$M_{11}=1$ $M_{12}=2$ $M_{21}=0$ $M_{22}=-1$ $C_{11}=1$ $C_{12}=-2$ $C_{21}=0$ $C_{22}=-1$

Work Step by Step

$ \begin{bmatrix} -1 &0 \\ 2& 1\\ \end{bmatrix} $ Minor $M_{ij}$of the entry $a_{ij}$ is the determinant of the matrix obtained by deleting the i-th row and j-th column of the matrix. To get $M_{11}$ we delete the second row and the second column and we get $M_{11}=1$. Use this method analogically to calculate $M_{12}$, $M_{21}$ and $M_{22}$. $M_{12}=2$ $M_{21}=0$ $M_{22}=-1$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=1$ $C_{12}=-2$ $C_{21}=0$ $C_{22}=-1$
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