If ax = b, then (a-1)ax = (a-1)b,
or x = (a-1)b (except when a is zero).
The value (a-1) is the inverse of a, and all non-zero real numbers have an inverse. It would be nice to have a similar idea for square matrices.
Say that
Ap = q
for column vectors p and q and n×n matrix A .
If all know are A and q, is it possible to figure out what p is? For example, say that you know that
A = 1 2 0 1, and that q = 5 2
Try to figure out p from the following. Keep changing the elements of p (only) until the result is q.
You can only change p in the above. Click on the = button to see the result with each change you make. Keep changing p, searching for the one that produces the result you want (i.e., q).
Did you figure it out?