Question

How do you solve using gaussian elimination or gauss-jordan elimination, `2x + y - z = -2`, `x + 3y + 2z = 4`, `3x + 3y - 3z = -10`?

Answer 1

`(x,y,z)=(4/3,-4/3,10/3)`

Explanation:

So let's make the matrix of the system, which is :

`[(2,1,-1,-2),(1,3,2,4),(3,3,-3,-10)]`

Now let's do our calculations :

`[(2,1,-1,-2),(1,3,2,4),(3,3,-3,-10)]rarr[(1,-2,-3,-6),(1,3,2,4),(0,-6,-9,-22)]rarr`

`[(1,-2,-3,-6),(0,5,5,10),(0,-6,-9,-22)]rarr[(1,-2,-3,-6),(0,1,1,2),(0,-6,-9,-22)]rarr`

`[(1,-2,-3,-6),(0,1,1,2),(0,0,-3,-10)]rarr[(1,0,-1,-2),(0,1,1,2),(0,0,1,10/3)]rarr`

`[(1,0,0,4/3),(0,1,0,-4/3),(0,0,1,10/3)]`

So we get : `(x,y,z)=(4/3,-4/3,10/3)`

(Just check my aritmetic, I tend to make mistakes)