is this matrix in reduced row echelon form \[ \begin{bmatrix}1 & 5 & 0 & \vert & 0 \\0 & 0 & 1& \vert & 4 \\0 & 0 & 0 & \vert & 1\end{bmatrix} \]
Question
is this matrix in reduced row echelon form
Solution
Yes, the given matrix is in reduced row echelon form.
A matrix is in reduced row echelon form if it satisfies the following conditions:
- All rows that contain only zeros are at the bottom of the matrix.
- The leading entry (also known as the pivot) of each non-zero row is 1.
- The pivot of each row is to the right of the pivot of the row above it.
- All entries in the column above and below a pivot are zero.
The given matrix satisfies all these conditions. Therefore, it is in reduced row echelon form.
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