Solve the system using Gauss or Gauss - Jordan elimination

I didn't know how to do this so I gave myself a quick lesson from here

Watch th video and work through the video example

then put it together with your knowledge of how elimination method to solve simultaneous equations works.

 

$$\begin{pmatrix}
2 &1&0&|-4 \\
0 &-2&4&|+0 \\
3 &0&-2&|-11 \\
\end{pmatrix}$$

First you need to get rid of the 3 in the bottom left corner.

1)  multiply R1 by3  and R3 by 2     WRITE down the new matrix

2)  R1-R3  replaces R3                    WRITE down the new matrix  (the 3 has been replaced with a 0)

NOW there is a 3 in R3, C2  You have to get rid of it

3) mult R2 by 3 and mult R3 by 2    WRITE down the new matrix

4) R2+R3 replaces R3                    WRITE down the new matrix  (the 6 has been replaced with a 0)

NOW the diagonal must only contain ones

5) Multiply R1 by 1/6,      Multiply R2 by -1/6         and multiply R3 by 20

 

And you should be able to take it from there

answer

x=-3,    y=2,   and    z=1