Answer
True
Work Step by Step
The matrix $\begin{bmatrix}1&3&|&-2\\0&1&|&5\\0&0&|&0\end{bmatrix}$ is in row echelon form because:
1) the element $a_{11}=1$ and all the other elements of column 1 are zeros
2) the first nonzero entry in row 2 is 1, only zeros are below it, and its position is at the right of the first 1 in the row above
3) the row containing all zeros to the left of the vertical bar is at the bottom.
So the statement is TRUE.
