Solving Linear Systems Using Matrices

[Bladesofhalo]

I have the following 3 equations
2x-y-4z=19
-x+3y-2z=-7
4x+2y+3z=37

Now I Have started the first step by writing it as a matrice
-1 3 -2 -7
2 -1 4 19
4 2 3 37

Now how do I proceed with this

 

[stapel]

What method(s) have you learned? Are you supposed to use row operations? Cramer's Rule? Something else?

When you reply, please show what you have tried and how far you have gotten. Thank you.

Eliz.

 

[Bladesofhalo]

We have learned the Elimination and Substitution methods, but she wants us to solve it using Matrices. Thats all the teacher expalined to us.

 

[Bladesofhalo]

It might be row operations, if Im not mistaken.

 

[pka]

\(\displaystyle \L \left[ {\begin{array}{ccc}
2 & { - 1} & { - 4} \\
{ - 1} & 3 & { - 2} \\
4 & 2 & 3 \\
\end{array}} \right]^{ - 1} = \frac{1}{{87}}\left[ {\begin{array}{ccc}
{13} & 5 & {14} \\
{ - 5} & {22} & 8 \\
{ - 14} & { - 8} & 5 \\
\end{array}} \right]\)