How would you solve these equation systems with matrices?

x + 4y + z = –10
3x – 3y + 6z = –21
x + 2y + 2z = –10

Question

How would you solve these equation systems with matrices?

x + 4y + z = –10
3x – 3y + 6z = –21
x + 2y + 2z = –10

anonymous · Answer

i would get rid to the x first then solve for one of the other variables

anonymous · Answer

Ok, I think I'll buy a book and learn to do matrices on my own. ^^

anonymous · Answer

oh my bad, i didnt even read the who question

anonymous · Answer

i just thought it said solve the system

anonymous · Answer

Yeah, well I know how to do that. But I can't construct a matrix because I haven't done that before. It's interesting and new to me.

anonymous · Answer

this is what we  have ( meaing the coefficient for each  linear equation)

anonymous · Answer

You put the equations into one equation, witch is called a matrix right?

anonymous · Answer

1   4 1          -10
3 -3 6            -21
1  2   2           -10

anonymous · Answer

So if I put the numbers:

 1   4 1        x         -10
[3 -3 6 ] *  [ y ] = [ -21 ]
 1   2 2        z         -10

Is that correct?

anonymous · Answer

Yes.  But then you make a matrix like$$\left[\begin{matrix}1 & 4 & 1 & -10 \ 3 & -3 & 6 & -21 \ 1 & 2 & 2 & -10\end{matrix}\right]$$and then solve using Gaussian elimination.