Echelon Form of a Matrix: Let us try to understand, what an echelon matrix is. Echelon matrices come in two forms: the row echelon form and the reduced row echelon form.
Row Echelon Form: A matrix is a Row Echelon is it satisfies the following conditions:
- The first non-zero element in each row, called the leading entry, is 1.
- Each leading entry is in a column to the right of the leading entry in the previous row
- All zero rows are at the bottom of the matrix
Both of the matrices shown below are examples of matrices in row echelon form.
Reduced Echelon Form: A matrix is known as reduced echelon form when it satisfies following conditions.
- The matrix satisfies conditions for a row echelon form
- The leading entry in each row is the only non-zero entry in its column