HP -15C Advanced Functions Handbook page 123

Section 4: Using Matrix Operations
121
Example: Use the residual correction program to calculate the
inverse of matrix A for
33 16 72
-24 -10 -57
-8 -4 -17
The theoretical inverse of A is
-29/3 -8/3 -32
8 5/2 51/2
8/3 2/3 9
Find the inverse by solving AX = B for X, where B is a 3 X 3
identity matrix.
First, enter the program from above. Then, in Run mode, enter the
elements into matrix A (the system matrix) and matrix B (the
right-hand, identity matrix). Press | GSB I [A] to execute the program.
Recall the elements of the uncorrected solution, matrix C:
C =
-9.666666881 -2.666666726 -32.00000071
8.000000167 2.500000046 25.50000055
2.666666728 0.6666666836 9.000000203
This solution is correct to seven digits. The accuracy is well within that
predicted by the equation on page 103.
(number of correct digits) ^ 9 - log(|| A|| ||C||) - log(3)« 4.8 .
Recall the elements of the corrected solution, matrix B:
B =
-9.666666667 -2.666666667 -32.00000000
8.000000000 2.500000000 25.50000000
2.666666667 0.6666666667 9.000000000
One iteration of refinement yields 10 correct digits in this case.