HP35S - Inverse of a 3x3 matrix (but also determinant, cross product, etc.)

[Roberto Volpi]

Dear Pedro

here quick examples as requested:

1) Determinant and inverse of following matrix:

1, 2, 3
4, 5, 6
7, 8, -9

Press:
1
ENTER
2
ENTER
3
XEQ M
ENTER

The calculator will ask for the 2nd row vector

Press:
4
ENTER
5
ENTER
6
R/S

The calculator will ask for the 3rd row vector

Press:
7
ENTER
8
ENTER
-9
R/S

The calculator will display "D=54" which is the determinant

Press: R/S

The calculator will display 2nd and 3rd row vectors of inverse matrix in 3D vector form.

Stack values will be as follows, with entries in FDISP for easier readability:

Stack t: 54 (which is the determinant value)
Stack z: [ -1+13/18, 7/9, -1/18 ] (1st row vector of inverse matrix)
Stack y: [ 1+4/9, -5/9, 1/9 ] (2nd row vector of inverse matrix)
Stack x: [-1/18, 1/9, -1/18] (3rd row vector of inverse matrix)

2) Cross product and angle of first 2 row vectors already inputed

Cross vector: RCL X, which gives [ -3, 6, -3 ]
Angle: Press XEQ M058, which gives Y=12.9331... as DEG

3) Cross product and angle of 2 3D vectors:

[ 3, 2, 1 ]
[ 7, 5, -2]

Press:
3
ENTER
2
ENTER
1
XEQ M003

The calculator will ask for the 2nd vector

Press:
7
ENTER
5
ENTER
-2
R/S

The calculator will display X= [ -9, 13, 1 ], which is the cross product
Press R/S, and the calculator will display Y=28.6482..., which is the angle in DEG mode

4) Determinant and inverse matrix made after adding a 3rd row vector to former example:

3rd row vector: [ 1, 2, -6 ]

Press:
XEQ M028
1
ENTER
2
ENTER
-6
R/S

The calculator will display D=11, which is the determinant

Press R/S

The calculator will display 2nd and 3rd row vectors of inverse matrix in 3D vector form.

Stack values will be as follows, with entries in FDISP for easier readability:

Stack t: 1 (which is the determinant value)
Stack z: [ -2+4/11, 1+3/11, -9/11 ] (1st row vector of inverse matrix)
Stack y: [ 3+7/11, -1+8/11, 1+2/11 ] (2nd row vector of inverse matrix)
Stack x: [ 9/11, -4/11, 1/11] (3rd row vector of inverse matrix)

Hope no typo is ruining these examples...