Chapter 11.2, Problem 4AYU

To determine

To explain: Whether the statement “The matrix $\left[\begin{array}{cc}1& 3\\ 0& 1\\ 0& 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$ is in row echelon form.” is true or false.

Answer to Problem 4AYU

The statement “The matrix $\left[\begin{array}{cc}1& 3\\ 0& 1\\ 0& 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$ is in row echelon form.” is true.

Explanation of Solution

Given information:

The statement “The matrix $\left[\begin{array}{cc}1& 3\\ 0& 1\\ 0& 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$ is in row echelon form.”

Consider the provided statement “The matrix $\left[\begin{array}{cc}1& 3\\ 0& 1\\ 0& 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$ is in row echelon form.”

The row echelon form of an augmented matrix is of the form that element of first row and first column should 1 and all other entries below it should be 0. Next the element of second row and second column should be 1 and all other entries below it should be 0 that is diagonal entries must be 1 and all other entries below it should be 0.

In the matrix provided diagonal entries of the left matrix are 1 and rest entries below it are 0. So, it is row echelon form.

Thus, the statement “The matrix $\left[\begin{array}{cc}1& 3\\ 0& 1\\ 0& 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$ is in row echelon form.” is true.