Chapter 11.4, Problem 61AYU

To determine

To show: The matrix has no inverse.

Answer to Problem 61AYU

Solution:

A is a singular matrix and has no inverse.

Explanation of Solution

Given:

  $A=\left[\begin{array}{ll}4\hfill & 2\hfill \\ 2\hfill & 1\hfill \end{array}\right]$

Calculation:

Step1 : Construction of $\left[A\mid I_n\right]$

  

Step 2 : Sequentially transforming the matrix $\left[A\mid I_n\right]$ into reduced row echelon form.

  

The matrix $\left[A\mid I_n\right]$ is sufficiently reduced for it to be clear that the identity matrix cannot appear to the left of the vertical bar. So A is a singular matrix and has no inverse.