# Chapter 3 - Determinants - 3.1 The Determination of a Matrix - 3.1 Exercises - Page 110: 15

#### Work Step by Step

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

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