HP 50g User Manual page 367

To see the intermediate steps in calculating and inverse, just enter the matrix A
from above, and press Y, while keeping the step-by-step option active in the
calculator's CAS. Use the following:
[[ 1,2,3],[3,-2,1],[4,2,-1]] `Y
After going through the different steps, the solution returned is:
What the calculator showed was not exactly a Gauss-Jordan elimination with
full pivoting, but a way to calculate the inverse of a matrix by performing a
Gauss-Jordan elimination, without pivoting. This procedure for calculating the
inverse is based on the augmented matrix (A
The calculator showed you the steps up to the point in which the left-hand half
of the augmented matrix has been converted to a diagonal matrix. From there,
the final step is to divide each row by the corresponding main diagonal pivot.
In other words, the calculator has transformed (A
-1
|A ].
Inverse matrices and determinants
Notice that all the elements in the inverse matrix calculated above are divided
by the value 56 or one of its factors (28, 7, 8, 4 or 1). If you calculate the
determinant of the matrix A, you get det(A) = 56.
We could write, A
⎡ 1
⎢
A 3
⎢
aug ( I )
⎢
4
⎣
-1
= C/det(A), where C is the matrix
⎡
⎢
C
⎢
⎢
14
⎣
2 3 1
2 1 0
2 1 0
)
aug n n
aug
0 8 8
⎤
⎥
7 13 8
⎥
⎥
6 8
⎦
0 0 ⎤
⎥
1 0 .
⎥
⎥
0 1
⎦
= [A |I
n n n n
) = [A |I
n n n n
.
].
], into [I
n n
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