Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 3 - Determinants - 3.3 Cofactor Expansions - Problems - Page 232: 2

Answer

The minors are: $M_{11}=4$ $M_{12}=2$ $M_{21}=-3$ $M_{22}=1$ The cofactors of the matrix A are: $C_{11}=4$ $C_{12}=-2$ $C_{21}=3$ $C_{22}=1$

Work Step by Step

$A=\begin{bmatrix} 1 & -3 \\ 2 & 4 \end{bmatrix}$ The minors are: $M_{11}=4$ $M_{12}=2$ $M_{21}=-3$ $M_{22}=1$ The cofactors of the matrix A are: $C_{11}=(-1)^{1+1}.4=4$ $C_{12}=(-1)^{1+2}.2=-2$ $C_{21}=(-1)^{2+1}.(-3)=3$ $C_{22}=(-1)^{2+2}.1=1$
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