Question

What is the row echelon form of this matrix?

Answer 1

The row echelon form of the matrix is presented as follows;

$\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}$

What is the row echelon form of a matrix?

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

$\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}$

The conditions of a matrix in the row echelon form are as follows;

1. There are row having nonzero entries above the zero rows.
2. The first nonzero entry in a nonzero row is a one.
3. The location of the leading one in a nonzero row is to the left of the leading one in the next lower rows.

Dividing Row 1 by -3 gives:

$\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}$

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}$

Subtracting Row 1 from Row 3 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}$

Adding Row 2 to Row 3 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}$

Dividing Row 2 by -2, and Row 3 by 18 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}$

The above matrix is in the row echelon form

Learn more about the row echelon form here:

brainly.com/question/14721322

#SPJ1