## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 3 - Determinants - 3.1 The Determination of a Matrix - 3.1 Exercises - Page 110: 23

#### Answer

$det(A)=0.002$

#### Work Step by Step

$\begin{bmatrix} -0.4 & 0.4 & 0.3 \\ 0.2 & 0.2 & 0.2 \\ 0.3 & 0.2 & 0.2 \end{bmatrix}$ $M_{11}= \begin{bmatrix} 0.2 &0.2 \\ 0.2& 0.2\\ \end{bmatrix} = 0.2(0.2)-0.2(0.2)=0$ $M_{12}= \begin{bmatrix} 0.2 &0.2 \\ 0.3& 0.2\\ \end{bmatrix}=0.2\times0.2-(0.3)0.2=-0.02$ $M_{13}= \begin{bmatrix} 0.2 &0.2 \\ 0.3& 0.2\\ \end{bmatrix}= 0.2\times0.2-(0.3)0.2=-0.02$ To calculate the cofactors, use the cofactor definition: $C_{ij}=(-1)^{ij}\times M_{ij}$ $C_{11}=0$ $C_{12}=0.02$ $C_{13}=-0.02$ $det(A)=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}$ $det(A)=-0.4(0)+0.4(0.02)+0.3\times(-0.02)$ $det(A)=0.002$

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