Matrix Inverse solving system of equations

• May 15th 2009, 04:26 AM
sydney
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
• May 15th 2009, 05:37 AM
mr fantastic
Quote:

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

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