# Math Help - Augmented Matrix Question

1. ## Augmented Matrix Question

Can someone please help with this question. Thanks

2. Originally Posted by ndcruz

Can someone please help with this question. Thanks
Using row-reduction:

$\left[\begin{array}{cccc}2 & 1 & | & 0 \\ 1 & -2 & | & -5 \\ \end{array}\right]$

Multiply R1 by 2:

$\left[\begin{array}{cccc}4 & 2 & | & 0 \\ 1 & -2 & | & -5 \\ \end{array}\right]$

Add R2 to R1:

$\left[\begin{array}{cccc}5 & 0 & | & -5 \\ 1 & -2 & | & -5 \\ \end{array}\right]$

Multiply R1 by 1/5:

$\left[\begin{array}{cccc}1 & 0 & | & -1 \\ 1 & -2 & | & -5 \\ \end{array}\right]$

Subtract R2 from R1:

$\left[\begin{array}{cccc}1 & 0 & | & -1 \\ 0 & 2 & | & 4 \\ \end{array}\right]$

Multiply R2 by 1/2:

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

Solution (-1, 2)