Chapter 7, Problem 65CR

To determine

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

Answer to Problem 65CR

Given matrix in reduced row-echelon form is $\left[\begin{array}{l}100\\ 010\\ 001\end{array}\right]$ .

Explanation of Solution

Given information: Given matrix is $\left[\begin{array}{l}1.53.64.2\\ 0.21.41.8\\ 2.04.46.4\end{array}\right]$ .

Calculation:

Let $A=\left[\begin{array}{l}1.53.64.2\\ 0.21.41.8\\ 2.04.46.4\end{array}\right]$ .

Operating $R_1\to 10R_1,R_2\to 10R_2,R_3\to 10R_3,$

  $A\sim \left[\begin{array}{l}153642\\ 21418\\ 204464\end{array}\right]$

Operating $R_1\to R_1-\frac{3}{4}{R}_3,$

  $A\sim \left[\begin{array}{l}03-6\\ 21418\\ 204464\end{array}\right]$

Operating $R_3\to R_3-10R_2,$

  $A\sim \left[\begin{array}{l}03-6\\ 21418\\ 0-96-116\end{array}\right]$

Operating $R_2\to \frac{1}{2}{R}_2,R_3\to R_3+32R_1,$

  $A\sim \left[\begin{array}{l}03-6\\ 179\\ 00-308\end{array}\right]$

Operating $R_1\to \frac{1}{3}{R}_1,R_3\to -\frac{1}{308}{R}_3,$

  $A\sim \left[\begin{array}{l}01-2\\ 179\\ 001\end{array}\right]$

  $R_1\leftrightarrow R_2,$

  $A\sim \left[\begin{array}{l}179\\ 01-2\\ 001\end{array}\right]$

Operating $R_1\to R_1-7R_2-23R_3,R_2\to R_2+2R_3,$

  $A\sim \left[\begin{array}{l}100\\ 010\\ 001\end{array}\right]$

Thus, the given matrix in reduced row-echelon form is $\left[\begin{array}{l}100\\ 010\\ 001\end{array}\right]$ .

Verification:

From graphing calculator, the result is

  

Hence, the result if verified.