Chapter 8, Problem 10RE

To determine

Write given matrix in Row-Echelon Form.

Answer to Problem 10RE

The row-echelon of matrix is

  $\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 1\\ 0& 0& -1\end{array}\right]$

Explanation of Solution

Given:

The matrix

  $\left[\begin{array}{ccc}4& 8& 16\\ 3& -1& 2\\ -2& 10& 12\end{array}\right]$

Consider the following matrix,

  $\left[\begin{array}{ccc}4& 8& 16\\ 3& -1& 2\\ -2& 10& 12\end{array}\right]$

Perform $–R_2+R_1$ ,

  $\left[\begin{array}{ccc}1& 9& 14\\ 3& -1& 2\\ -2& 10& 12\end{array}\right]$

Perform $–3R_1+R_2$ .

  $\left[\begin{array}{ccc}1& 9& 14\\ 0& -28& -40\\ -2& 10& 12\end{array}\right]$

Perform $2R_1+R_3$ .

  $\left[\begin{array}{ccc}1& 9& 14\\ 0& -28& -40\\ 0& 28& 40\end{array}\right]$

Perform $R_2+R_3$ .

  $\left[\begin{array}{ccc}1& 9& 14\\ 0& -28& -40\\ 0& 0& 0\end{array}\right]$

Perform $–\frac{1}{28}{R}_2$ ,

  $\left[\begin{array}{ccc}1& 9& 14\\ 0& 1& \frac{10}{7}\\ 0& 0& 0\end{array}\right]$

Hence row-echelon of matrix is

  $\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 1\\ 0& 0& -1\end{array}\right]$