# Thread: Matrix Inverse solving system of equations

1. ## Matrix Inverse solving system of equations

Given
A =
1 0 -2
3 1 -6
0 1 1

I have worked out the inverse matrix and I have to use it to solve the system of equations
3x-y = 5
7x - 2y + 2z = 3
3x - y + z = 7

I can see that this is the inverse matrix, with rows 1 and 2 swapped (and -R1) but I don't know how this affects solving the equations. I have to use the inverse to solve. I really would like to understand what's happening here, rather tan just the answer. I'd appreciate any help.

Thanks

2. Originally Posted by sydney
Given
A =
1 0 -2
3 1 -6
0 1 1

I have worked out the inverse matrix and I have to use it to solve the system of equations
3x-y = 5
7x - 2y + 2z = 3
3x - y + z = 7

I can see that this is the inverse matrix, with rows 1 and 2 swapped (and -R1) but I don't know how this affects solving the equations. I have to use the inverse to solve. I really would like to understand what's happening here, rather tan just the answer. I'd appreciate any help.

Thanks
Re-write your equations as:

7x - 2y + 2z = 3
-3x + y = -5
3x - y + z = 7

In matrix form you have $\displaystyle AX = B \Rightarrow X = A^{-1} B$ where A is the coeffcient matrix. And the given matrix is the inverse of the coefficient matrix ....

3. ## Thanks

Thank you very much. I knew it had to do with something like that but I just hadn't mutliplied R2 equation thru by the negative!

Really appreciate your help.