Q 4. - Precalculus Enhanced with Graphing Utilities

Question

Determine whether the given statement is true or false.

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.

Step-by-Step Solution

Answer

Yes, the given statement is true.

Step 1. Given information.

The given matrix is $\left[\begin{array}{cc}1& 3 |\\ 0& 1 |\\ 0& 0 |\end{array}\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$.

Step 2. The task is to answer whether a given statement is true or false.

$\left[\begin{array}{cc}1& 3 |\\ 0& 1 |\\ 0& 0 |\end{array}\begin{array}{c}-2\\ 5\\ 0\end{array}\right]$

In the above matrix, we can see that below $1$ and to the left of $1$ are zeros, so this matrix is in row echelon form.

Step 3. Simplified answer.

Hence, the given statement is true.