A-1 A p = A-1 p 1 -2 0 1 1 2 0 1 p = 1 -2 0 1 5 2
I p = 1 -2 0 1 5 2
p = 1 -2 0 1 5 2 = 1 2
This is (hopefully) the same answer you got for p by trial and error a few pages ago. If A is non-singular (has an inverse) and Ap = q, then p = A-1q.
The inverse of a non-singular square matrix is unique.
One way to see this is that there is only one
column matrix p that is the solution to
It might look like computing A-1 is a useful thing to do. In fact, A-1 is more useful in discussions about matrices and transformations than it is in actual practice. Almost never do you really want to compute a matrix inverse.
For example, say that a column matrix p represents a
point in a computer graphic world.
The viewpoint changes, and the column matrix is transformed to