Question

[1 0 0 0 ] [0 0 0 0 ] [0 1 5 1 ] A matrix is given. Determine whether the matrix is in row-echelon form.

Answer 1

The matrix is not in row-echelon form.

Step-by-step explanation:

A matrix is in row-echelon form if it satisfies the following conditions:

1. All rows consisting of only zeros are at the bottom.
2. The first non-zero entry in each row (also known as the leading entry) is to the right of the leading entry in the row above it.
3. All entries below the leading entry in a column are zeros.

Looking at the given matrix:

[1 0 0 0]
[0 0 0 0]
[0 1 5 1]

The matrix does not meet the second condition of row-echelon form because the leading entry in the third row (1) is to the left of the leading entry in the second row (0). Therefore, the matrix is not in row-echelon form.