Question

Represent the system of equations as a matrix.

x+2y+z=-5
2x-y-3z=5
x+y+2z=0

Perform elementary row operations on the matrix to transform it into reduced row echelon form.
What is the reduced row echelon form of the matrix?
Enter your answer by filling in the boxes.

Answer 1

Explanation:

x+2y+z=-5

2x-y-3z=5

x+y+2z=0

The given system of equations is a 3×4 matrix:

`\left[\begin{array}{ccccc}1&2&1&|&-5\\2&-1&-3&|&5\\1&1&2&|&0\end{array}\right]`

We need to find the echelon form of the rows of this matrix

Multiply line 1 by (-2) and add it to line 2:

`\left[\begin{array}{ccccc}1&2&1&|&-5\\0&-5&-5&|&15\\1&1&2&|&0\end{array}\right]`

Multiply line 1 by (-1) and add it to line 3:

`\left[\begin{array}{ccccc}1&2&1&|&-5\\0&-5&-5&|&15\\0&-1&1&|&5\end{array}\right]`

Divide the line 2 by (-5) and add it to row 3:

`\left[\begin{array}{ccccc}1&2&1&|&-5\\0&-5&-5&|&15\\0&0&2&|&2\end{array}\right]`

Consequently, the matrix in the form of an echelon of rows has the form:

`\left[\begin{array}{ccccc}1&2&1&-5\\0&-5&-5&15\\0&0&2&2\end{array}\right]`