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: 13

Answer

$M_{11}=4$ $M_{12}=3$ $M_{13}=2$ $M_{14}=1$ $C_{11}=4$ $C_{12}=-3$ $C_{13}=-2$ $C_{14}=1$

Work Step by Step

$ \begin{bmatrix} 1 &2 \\ 3& 4\\ \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 $M_{11}=4$. Use this method analogically to calculate $M_{12}$, $M_{21}$ and $M_{22}$. $M_{12}=3$ $M_{21}=2$ $M_{22}=1$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=4$ $C_{12}=-3$ $C_{21}=-2$ $C_{22}=1$
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