Chapter 7, Problem 64CR

To determine

To write: The given matrix in reduced row-echelon form and to verify the result using a graphing utility.

Answer to Problem 64CR

Given matrix in reduced row-echelon form is $\left[\begin{array}{l}10-30\\ 0150\\ 0001\end{array}\right]$ .

Explanation of Solution

Given information: Given matrix is $\left[\begin{array}{l}1122\\ -1035\\ -2-2-44\end{array}\right]$ .

Calculation:

Let $A=\left[\begin{array}{l}1122\\ -1035\\ -2-2-44\end{array}\right]$ .

Operating $R_2\to R_2+R_1,R_3\to R_3+2R_1,$

  $A\sim \left[\begin{array}{l}1122\\ 0157\\ 0008\end{array}\right]$

Operating $R_3\to \frac{1}{8}{R}_3,$

  $A\sim \left[\begin{array}{l}1122\\ 0157\\ 0001\end{array}\right]$

Operating $R_2\to R_2-7R_1,R_1\to R_1-2R_3,$

  $A\sim \left[\begin{array}{l}1120\\ 0150\\ 0001\end{array}\right]$

Operating $R_1\to R_1-R_2,$

  $A\sim \left[\begin{array}{l}10-30\\ 0150\\ 0001\end{array}\right]$

Thus, the given matrix in reduced row-echelon form is $\left[\begin{array}{l}10-30\\ 0150\\ 0001\end{array}\right]$ .

Verification:

  

Hence, the result if verified.