Answer
Reduced Row-Echelon Form
Work Step by Step
There are 3 main rules for a matrix to be in row echelon form:
1. A row of all 0s must be at the bottom.
2. The first non-zero entry in a row must be a 1. This is called the leading 1.
3. The leading 1 in a higher row must be in a column further to the left than a lower leading 1.
For a matrix to be in reduced row echelon form, the rules for row echelon form must be met with the addition of this rule:
4. Every column with a leading 1 must have all 0s above the leading 1.
When given the following conditions, the matrix will be:
$\begin{bmatrix}
1 & 0 \\
0 & 1 \\
\end{bmatrix}$
The above matrix satisfies rules 1 - 4, so the matrix is in reduced row-echelon form.
