## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 3 - Determinants - 3.1 The Determination of a Matrix - 3.1 Exercises - Page 110: 16

#### Answer

(a) The minors are given by: \begin{align*} M_{11}&=-17, \quad M_{12}=-52, \quad M_{13}=-54,\\ M_{21}&=-18, \quad M_{22}=16, \quad M_{23}=5,\\ M_{31}&=-2, \quad M_{32}=-15, \quad M_{33}=-33. \end{align*} (b) The cofactors, are given by: \begin{align*} C_{11}&=-17, \quad C_{12}=52, \quad C_{13}=-54,\\ C_{21}&=18, \quad C_{22}=16, \quad C_{23}=-5,\\ C_{31}&=-2, \quad C_{32}=15, \quad C_{33}=-33. \end{align*}

#### Work Step by Step

Given $$\left|\begin{array}{rrr}{-3} & {4} & {2} \\ {6} & {3} & {1} \\ {4} & {-7} & {-8}\end{array}\right|.$$ (a) The minors are given by: \begin{align*} M_{11}&=-17, \quad M_{12}=-52, \quad M_{13}=-54,\\ M_{21}&=-18, \quad M_{22}=16, \quad M_{23}=5,\\ M_{31}&=-2, \quad M_{32}=-15, \quad M_{33}=-33. \end{align*} (b) The cofactors, are given by: \begin{align*} C_{11}&=-17, \quad C_{12}=52, \quad C_{13}=-54,\\ C_{21}&=18, \quad C_{22}=16, \quad C_{23}=-5,\\ C_{31}&=-2, \quad C_{32}=15, \quad C_{33}=-33. \end{align*}

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