Chapter 8.1, Problem 46E

To determine

Identify the matrix

Answer to Problem 46E

Row-Echelon form Not Reduced Row-Echelon Form.

Explanation of Solution

Given information:

Find out whether the matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form.

  $\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 2\\ 0& 0& 1& 0\end{array}\right]$

Calculation:

Properties of Row-Echelon form and Reduced Row-Echelon Form

1. Any rows consisting entirely of zeros occur at the bottom of the matrix.

2. For each row that does not consist entirely of zeros, the first nonzero entry is 1 (called a leading 1).

3. For two successive (nonzero) rows, the leading 1 in the higher row is farther to the left than the leading 1 in the lower row.

A matrix in row-echelon form is in reduced row-echelon form when every column that has a leading 1 has zeros in every position above and below its leading 1.

The given matrix satisfies all properties of row-echelon not Reduced Row-Echelon Form.