Chapter B, Problem 1PE

To determine

The matrix after the indicated operation

Answer to Problem 1PE

Solution:

After performing the operation $R_1\leftrightarrow R_2$ , the matrix becomes $\left[\begin{array}{cc}1& -\frac{3}{2}\\ 2& 2\end{array}|\begin{array}{c}5\\ 5\end{array}\right]$

Explanation of Solution

Given:

  $\left[\begin{array}{cc}2& 2\\ 1& -\frac{3}{2}\end{array}|\begin{array}{c}5\\ 5\end{array}\right]$

Formula used:

Rules:

a) $R_1\leftrightarrow R_2$ is an operation interchanging Rows 1 & 2.

b) $a{R}_1$ means multiplying row 1 with a number $a$ .

Calculations:

We are given

  $\left[\begin{array}{cc}2& 2\\ 1& -\frac{3}{2}\end{array}|\begin{array}{c}5\\ 5\end{array}\right]$

  $R_1\leftrightarrow R_2$

  $\left[\begin{array}{cc}1& -\frac{3}{2}\\ 2& 2\end{array}|\begin{array}{c}5\\ 5\end{array}\right]$

Conclusion:

After performing the operation $R_1\leftrightarrow R_2$ , the matrix becomes $\left[\begin{array}{cc}1& -\frac{3}{2}\\ 2& 2\end{array}|\begin{array}{c}5\\ 5\end{array}\right]$