p | = | A-1 | q |
---|
p | = | ![]() |
1 -2 0 1 |
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5 2 |
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= | ![]() |
1 2 |
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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
What is (AB) (B-1 A-1) ?