Solving a system with the inverse of a matrix.

[thatguythere]

Homework Statement

a)Use Gauss-Jordan elimination to find the inverse of A =
[ 2 1 4 ]
[ 1 1 2 ]
[ -2 -3 -2 ]

b) Use the result from part a) to find the solution of the following system.

5x+2y-3z = 5
x+y-z = -1
-3x-y+2z = 2

Homework Equations

The Attempt at a Solution

My problem is not with part a), I quite easily found the inverse of the matrix. What I am not understanding is what exactly they are asking me to do for part b). How can I use the inverse of one matrix to solve for another? Any help is greatly appreciated.

 

[rock.freak667]

If you change

5x+2y-3z = 5
x+y-z = -1
-3x-y+2z = 2

into a matrix equation in the form of Bx=C, what would B, X and C be?

 

[Dick]

If you change

5x+2y-3z = 5
x+y-z = -1
-3x-y+2z = 2

into a matrix equation in the form of Bx=C, what would B, X and C be?

I'm with thatguythere. I can't see that the matrix in part b) is related in any simple way to the matrix in part a). I'm suspecting the somebody goofed when assembling the problem.

 

[thatguythere]

I contacted my TA and it is indeed a mistake. It should be
2x + y + 4z = 5
x + y + 2z = -1
-2x -3y -2z = 2
I should be able to manage now, thanks.

 

[rock.freak667]

I'm with thatguythere. I can't see that the matrix in part b) is related in any simple way to the matrix in part a). I'm suspecting the somebody goofed when assembling the problem.

Ah well, I didn't calculate the inverse, so I assumed it one of those problems where the matrix equation would be A^-1x=B