Question

[ 0 0 1 0 0 ] [ 0 0 0 1 0 ] [ 0 0 0 1 0 ] A matrix is given. Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced row-echelon form. STEP 1: Check rows consisting entirely of zeros Do all rows (if any) consisting entirely of zeros occur at the bottom of the matrix? a. Yes b. No c. There are no rows consisting entirely of zeros

Answer 1

A matrix is said to be in row-echelon form if the given conditions are satisfied. The given matrix is in row-echelon form but not in reduced row-echelon form.

Step-by-step explanation:

A matrix is said to be in row-echelon form if:

1. Any row containing only zeros is at the bottom.
2. In each non-zero row, the leftmost non-zero entry is equal to 1.
3. Among all non-zero entries in a column, the leftmost entry (called a pivot) is the only non-zero entry in its column.
4. The pivot in any row below a row containing a pivot is to the right of the pivot in the row above it.

Looking at the given matrix, each row containing only zeros occurs at the bottom, and the leftmost non-zero entry in each non-zero row is indeed 1. However, the pivot in the third row is not to the right of the pivot in the second row, so the matrix is not in reduced row-echelon form.