## Algebra and Trigonometry 10th Edition

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: $\begin{bmatrix} 1 & n \\ n & 1 \\ \end{bmatrix}$ where $n \ne 0$ Since rule 2 is not followed in the matrix, the matrix is neither row-echelon form nor reduced row-echelon form.