Chapter 11.2, Problem 4AYU

True or False The matrix $\left[\begin{array}{c}1\\ 0\\ 0\end{array}\begin{array}{c}3\\ 1\\ 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$ is in row echelon form.

To determine

Check whether the given statement is true or false: The matrix $\left(\begin{array}{c}1\\ 0\\ 0\end{array}\begin{array}{c}3\\ 1\\ 0\end{array}|\begin{array}{c}-2\\ 5\\ 0\end{array}\right)$ is in row echelon form.

Answer to Problem 4AYU

Solution:

True.

Explanation of Solution

A matrix is in row echelon form if:

a. The entry in row 1, column 1 is 1 and the entries below $a_{11}$ are only 0.

b. The first nonzero entry in each row after the 1^st row is 1, entries below this 1 are 0 and the entries to the right of the first nonzero entry in any row above are 1.

c. Any rows that contain all 0’s to the left of the vertical bar appear at the bottom.

So the given matrix is in row echelon form.

Hence the given statement is true.