Chapter 7, Problem 80RE

To determine

To write: the matrix in reduced row echelon form using matrix capabilities of a graphing utility.

Answer to Problem 80RE

The reduced row echelon form of the matrix is:

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

Explanation of Solution

Given information:

Given matrix

  $\left[\begin{array}{ccc}4.1& 8.3& 1.6\\ 3.2& -1.7& 2.4\\ -2.3& 1.0& 1.2\end{array}\right]$

Calculation:

To make calculations easy we multiply each term of the matrix by 10. Then the matric reduced to

  $\begin{array}{l}B=10\left[\begin{array}{ccc}4.1& 8.3& 1.6\\ 3.2& -1.7& 2.4\\ -2.3& 1.0& 1.2\end{array}\right]\\ =\left[\begin{array}{ccc}41& 83& 16\\ 32& -17& 24\\ -23& 10& 12\end{array}\right]\end{array}$

Select the matrix from the MATRIX EDIT menu and enter the dimensions.

  

The center portion of the matrix editor displays up to three rows and three columns of a matrix.

The display of the matrix is shown below,

  

This is a $3\times 3$ matrix.

To display the contents of a matrix on the home screen, select the matrix from the MATRIX NAMES menu, and then press ENTER.

The matrix will be displayed as below,

  

To find the reduced row-echelon form of the matrix,

Press 2^nd, MATRIX and MATH, select rref.

The screen is shown below:

  

Press the option rref of the matrix $\text{A}$ and then ENTER, we obtain the row-echelon of the matrix.

  

Therefore the reduced row echelon form of the matrix is:

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