Find the inverse matrix of A, then use this inverse to solve system of equation.
A is a given 3 x 3 matrix and the system of equations is 3 equations in 3 unknowns.
The Attempt at a Solution
I have found the inverse of A using an augmented identity matrix. Checked this inverse by taking product of A and inverse A and got identity matrix.
The system of equations is something like this (these are not the actual values):
6x - 2y = 10
14x - 4y + 4z = 3
6x - 2y + 2z = 14
Now when I take the product of inverse A and [10 3 14] to solve for x, y and z, putting these values into the original equations does not hold.
I was told to try re-arrange the equations and compare to the inverse matrix, but can't seem to find a solution.
Note that by swapping 2 rows in my inverse matrix the co-effiecients of the unkowns in the system of equations are the same as the entries in the matrix.
Gee I hope that made sense.