Chapter 2, Problem 11RP

Explanation of Solution

Finding the inverse of the given matrix using Gauss–Jordan method:

Consider the following matrix,

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

The objective is to find the inverse of the given matrix using Gauss- Jordan method.

To find the inverse of the matrix $A$ , first write the matrix in the form $A|I_m$ as shown below:

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

Now use the elementary row operations to transform $A|I_m$ into $I_m|B$.

Here, $B=A^{-1}$

$\left[\begin{array}{l}\text{1 0 2}\\ \text{0 1 0}\\ \text{0 1 1}\end{array}\right]\left[\begin{array}{l}\text{1 0 0}\\ \text{0 1 0}\\ \text{0 0 1}\end{array}\right]\stackrel{R_3\to R_3-R_2}{\to }\left[\begin{array}{l}\text{1 0 2}\\ \text{0 1 0}\\ \text{0 0 1}\end{array}\right][\begin{array}{l}\text{1 0 0}\\ \end{array}$