Chapter 7, Problem 61CR

To determine

To write: The matrix in row echelon form.

Answer to Problem 61CR

The matrix in row echelon form is:

  $\left[\begin{array}{l}123\\ 011\\ 001\end{array}\right]$ .

Explanation of Solution

Given information: The given matrix is:

  $\left[\begin{array}{l}011\\ 123\\ 222\end{array}\right]$ .

Calculation: The given matrix is:

  $\left[\begin{array}{l}011\\ 123\\ 222\end{array}\right]$ .

Use row operation to get a diagonal of $1$ ’s and zeros to the left of the diagonal.

Interchange the first and second row:

  $\left[\begin{array}{l}123\\ 011\\ 222\end{array}\right]$

  $\begin{array}{l}{R}_3\to R_3-2R_1\\ \left[\begin{array}{l}123\\ 011\\ 0-2-4\end{array}\right]\end{array}$

  $\begin{array}{l}{R}_3\to R_3+2R_2\\ \left[\begin{array}{l}123\\ 011\\ 00-2\end{array}\right]\end{array}$

  $\begin{array}{l}{R}_3\to -\frac{1}{2}{R}_3\\ \left[\begin{array}{l}123\\ 011\\ 001\end{array}\right]\end{array}$

Thus the matrix in row echelon form is:

  $\left[\begin{array}{l}123\\ 011\\ 001\end{array}\right]$ .