(35S) Determinant of a 3x3 matrix (plus cross product): the shortest way.

[Roberto Volpi]

Taking advantage of the HP35S vector support, a determinant of a 3x3 squared matrix can be computed with just 10 lines of programs:

001 LBL M
002 XEQ X
003 STO G
004 SF 10
005 (EQN) 3RD VECTOR
006 CF 10
007 (EQN) [REGZ, REGY, REGX]*
008 RCL G
009 x
010 RTN

* to insert REGX in program mode press EQN, R down, and select X

INSTRUCTIONS:

The elements of our 3x3 matrix will be input as row vectors, just by typing the values separated by ENTER.

EX. calculate the determinant of the following 3x3 matrix:

[3, 5, 2
9, 7, 2
11, 0, 0]

- input the 1st row: 3 ENTER 5 ENTER 2
- press XEQ M and the HP35S will display: 2ND VECTOR
- input the 2nd row: 9 ENTER 7 ENTER 2
- press R/S and the HP35S will display: 3RD VECTOR
- input the 3rd row: 11 ENTER 0 ENTER ENTER (as the "0" is repeated)
- press R/S and the HP35S will display the result: -44

It does not work? Well, also the subroutine X needs to be inserted.

It is a short standalone program of just 10 lines to compute the cross product of a 2 vectors of 3 elements.

001 LBL X
002 SF 10
003 STO C
004 R down
005 STO B
006 R down
007 (EQN) 2ND VECTOR
008 CF 10
009 (EQN) [BxREGX-CxREGY,CxREGZ-REGTxREGX,REGTxREGY-BxREGZ]
010 RTN


INTRUCTIONS:

The elements of our vectors will be input just by typing the values separated by ENTER.

EX. calculate the cross products of these 2 vectors:
[3, 5, 2] and [9, 7, 2]

- input the 1st vector: 3 ENTER 5 ENTER 2
- press XEQ X and the HP35S will prompt: 2ND VECTOR
- input the 2nd vector: 9 ENTER 7 ENTER 2
- press R/S and the HP35S will display the result: [-4, 12, -24]

Enjoy!

[Thomas Klemm]

Somewhat related from HP 35s - my first thoughts: Message #20:

Code:

X001 LBL X
X002 ABS
X003 CLx
X004 LASTx
X005 RDN
X006 RDN
X007 [
      [0,[0,0,-1]*REGT,[0,1,0]*REGT]*REGZ,
      [[0,0,1]*REGT,0,[-1,0,0]*REGT]*REGZ,
      [[0,-1,0]*REGT,[1,0,0]*REGT,0]*REGZ
     ]
X008 REGZ
X009 RDN
X010 RTN

Lines 2-4 and 8-9 could be omitted. They copy T to Z and X to LASTx.

Now that we have the cross-product of two vectors it's easy to calculate the determinant: just calculate the scalar product with the third vector.

[Thomas Klemm]

You might also be interested in these links:

• A Matrix Multi-Tool for the HP 35s Programmable Calculator
• An Extension for Stefan's Matrix Multi-Tool Program
• Palmer's Matrix Multi-Tool Extension
  

[Roberto Volpi]

(06-26-2022 09:01 AM)Thomas Klemm Wrote:  You might also be interested in these links:

• A Matrix Multi-Tool for the HP 35s Programmable Calculator
• An Extension for Stefan's Matrix Multi-Tool Program
• Palmer's Matrix Multi-Tool Extension
  

The list of related items may be in fact endless.

Matrices are an interesting subject and lot of HP35S users have submitted great programs to add matrix calculation features, à la HP15C.