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

1 Answer

Answer:

#(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)