We convert the system of equations:
to the matrix equation:
I will assume that you know how to find the inverse of the
coefficient matrix. If not post again asking how. It is
Now we left multiply both sides of the matrix equation by
the inverse of the coefficient matrix:
I will also assume that you know how to multiply
matrices. If you don't, post again asking how.
Multiplying the matrices on the right and
multiplying the first two on the left, we get:
That's the identity matrix on the left, which is what you
always get when you multiply a matrix by its inverse.
Multiplying the identity matrix by the column matrix of
variables on the left we get
So a = 3, b= 1, c = 2.
Even though I did the entire problem, working with the
entire matrix equation, you can see that you can use a
shortcut of just doing the right side only, which is to
left-multiply the inverse of the coefficient matrix by
the column matrix of constants. That's because in every
case the left side will be the same as above.
Edwin
