Question

[ 1 3 0 1 0 0 ] [ 0 1 0 4 0 0 ] [ 0 0 0 1 1 2 ] [ 0 0 0 1 0 0 ] A matrix is given. Determine whether the matrix is in row-echelon form.

Answer 1

The given 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 entirely of zeros are at the bottom.
2. In each row, the first non-zero element (called the leading element) is to the right of the leading element of the row above it.
3. All entries below a leading element are zero.

Looking at the given matrix:

• Row 3 has all zeros after the first non-zero element, so condition 3 is satisfied.
• Row 4 has all zeros after the first non-zero element, so condition 3 is satisfied.
• Row 2 has its leading element to the right of the leading element of row 1, so condition 2 is satisfied.
• Row 1 does not have its leading element to the right of the leading element of row 2, so condition 2 is not satisfied.

Since the given matrix does not satisfy all the conditions for row-echelon form, it is not in row-echelon form.