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+--- Thread: (35S) Determinant of a 3x3 matrix (plus cross product): the shortest way. (/thread-18512.html)
(35S) Determinant of a 3x3 matrix (plus cross product): the shortest way. - Roberto Volpi - 06-26-2022 07:42 AM
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!
RE: (35S) Determinant of a 3x3 matrix (plus cross product): the shortest way. - Thomas Klemm - 06-26-2022 08:52 AM
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 RTNNow 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.
RE: (35S) Determinant of a 3x3 matrix (plus cross product): the shortest way. - Thomas Klemm - 06-26-2022 09:01 AM
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
RE: (35S) Determinant of a 3x3 matrix (plus cross product): the shortest way. - Roberto Volpi - 06-26-2022 09:07 AM
(06-26-2022 09:01 AM)Thomas Klemm Wrote: You might also be interested in these links:
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.