Chapter 16.6, Problem 3WE

To determine

To Find: The value of inverse of:

  $\left[\begin{array}{cc}4& 6\\ 2& 3\end{array}\right]$

If exists.

Answer to Problem 3WE

Inverse of given matrix does not exist.

Explanation of Solution

Given: $\left[\begin{array}{cc}4& 6\\ 2& 3\end{array}\right]$

Formula Used:

1. Determinant formula:

  $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-cb$

Finding the determinant:

  $\left|\begin{array}{cc}4& 6\\ 2& 3\end{array}\right|=(4)(3)-(2)(6)=12-12=0$

Determinant is zero, therefore the inverse does not exist.