Question

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

Answer 1

A matrix is said to be in reduced row-echelon form if it satisfies certain conditions. The given matrix satisfies these conditions.

Step-by-step explanation:

A matrix is said to be in reduced row-echelon form if it satisfies the following conditions:

1. The leftmost non-zero entry in each row, called a pivot, is equal to 1.
2. The pivot in each row is to the right of the pivot in the row above it.
3. All the entries below and above the pivot are zero.
4. All rows consisting entirely of zeros are at the bottom of the matrix.

Looking at the given matrix, we can see that it satisfies all these conditions. Therefore, the matrix is in reduced row-echelon form.