Question

For the following linear system, put the augmented coefficient matrix into reduced row-echelon form.

x1 − 2x2 + 3x3 + 2x4 + x5 = 10

2x1 − 4x2 + 8x3 + 3x4 + 10x5 = 7

3x1 − 6x2 + 10x3 + 6x4 + 5x5 = 27

Answer 1

The augmented matrix is

$\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\2&-4&8&3&10&7\\3&-6&10&6&5&27\end{array}\right]$

Add -2(row 1) to row 2, and add -3(row 1) to row 3:

$\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\0&0&1&-1&8&-13\\0&0&1&0&2&-3\end{array}\right]$

Add -1(row 2) to row 3:

$\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\0&0&1&-1&8&-13\\0&0&0&1&-6&10\end{array}\right]$

Add row 3 to row 2:

$\left[\begin{array}{ccccc|c}1&-2&3&2&1&10\\0&0&1&0&2&-3\\0&0&0&1&-6&10\end{array}\right]$

Add -3(row 2) to row 1, and add -2(row 3) to row 1:

$\left[\begin{array}{ccccc|c}1&-2&0&0&7&-1\\0&0&1&0&2&-3\\0&0&0&1&-6&10\end{array}\right]$