Chapter 2.6, Problem 2P

Explanation of Solution

Finding the determinant:

Consider the following matrix,

$A=\left[\begin{array}{l}\text{1 0 0 0}\\ \text{0 2 0 0}\\ \text{0 0 3 0}\\ \text{0 0 0 5}\end{array}\right]$

The first-row cofactors are given below:

$\begin{array}{l}{A}_{11}=\left[\begin{array}{l}\text{2 0 0}\\ \text{0 3 0}\\ \text{0 0 5}\end{array}\right]\\ \end{array}$

Therefore, we get

$\begin{array}{l}\det (A_{11}\end{array}$