# Solution With The Inverse Matrix; Solution By "division" Of Matrices - HP 50g User Manual

Graphing calculator.

Compare these three solutions with the ones calculated with the numerical
solver.

## Solution with the inverse matrix

The solution to the system A x = b, where A is a square matrix is x = A
This results from multiplying the first equation by A
-1
definition, A
A = I, thus we write I x = A
-1
= A
b.
For the example used earlier, namely,
we can find the solution in the calculator as follows:
which is the same result found earlier.

### Solution by "division" of matrices

While the operation of division is not defined for matrices, we can use the
calculator's / key to "divide" vector b by matrix A to solve for x in the matrix
equation A x = b. This is an arbitrary extension of the algebraic division
operation to matrices, i.e., from A x = b, we dare to write x = b/A
(Mathematicians would cringe if they see this!) This, of course is interpreted as
-1
(1/A) b = A
b, which is the same as using the inverse of A as in the previous
section.
-1
2x
+ 3x
–5x
1
2
3
x
– 3x
+ 8x
1
2
3
2x
– 2x
+ 4x
1
2
-1
-1
, i.e., A
b. Also, I x = x, thus, we have, x
= 13,
= -13,
= -6,
3
-1
b.
-1
A x = A
b. By
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