# HP Forums

You're currently viewing a stripped down version of our content. View the full version with proper formatting.

Determinant of a 3 x 3 Matrix

The following program calculates a determinant of a matrix:

[ [ K, N, Q ]
[ L, O, R ]
[ M, P, S ] ]

The determinant is K*O*S + N*R*M + Q*L*P - M*O*Q - P*R*K - S*L*N.

Enter the elements in columns.

Program HP 35S: Determinant

Code:
```D001 LBL D D002 SF 10 D003 "DET 3x3" D004 CF 10 D005 INPUT K D006 INPUT L D007 INPUT M D008 INPUT N D009 INPUT O D010 INPUT P D011 INPUT Q D012 INPUT R D013 INPUT S D014 RCL K D015 RCL* O D016 RCL* S D017 RCL N D018 RCL* R D019 RCL* M D020 + D021 RCL Q D022 RCL* L D023 RCL* P D024 + D025 RCL M D026 RCL* O D027 RCL* Q D028 - D029 RCL P D030 RCL* R D031 RCL* K D032 - D033 RCL S D034 RCL* L D035 RCL* N D036 - D037 RTN```

Examples:

[ [ -3, 3, 2 ]
[ 5, 4, -1 ]
[ 2, 1, 4 ] ]
Determinant: -123

[ [ 5, 0, 7 ]
[ -2, 4, -1 ]
[ -3, 11, 6 ] ]
Determinant: 105

Cramer's Rule

Cramer's Rule solves the linear system:

[[ A, D, G ] [[ x ] = [[ X ]
[ B, E, H ] [ y ] = [ Y ]
[ C, F, I ]] [ z ]] = [ Z ]]

x = U, y = V, z = W, T = determinant of the coefficients

Program HP 35S: Cramer's Rule

Code:
```C001 LBL C C002 GTO C027 C003 RCL K     // determinant calculation C004 RCL* O C005 RCL* S C006 RCL N C007 RCL* R C008 RCL* M C009 + C010 RCL Q C011 RCL* L C012 RCL* P C013 + C014 RCL M C015 RCL* O C016 RCL* Q C017 - C018 RCL P C019 RCL* R C020 RCL* K C021 -  C022 RCL S C023 RCL* L C024 RCL* N C025 -  C026 RTN C027 SF10  // input numbers into the system C028 "COL 1" C029 INPUT A C030 STO K C031 INPUT B C032 STO L C033 INPUT C C034 STO M C035 "COL 2" C036 INPUT D C037 STO N C038 INPUT E C039 STO O C040 INPUT F C041 STO P C042 "COL 3" C043 INPUT G C044 STO Q C045 INPUT H C046 STO R C047 INPUT I C048 STO S C049 "VECTOR"  C050 INPUT X C051 INPUT Y C052 INPUT Z C053 XEQ C003 C054 STO T C055 "DET=" C056 VIEW T C057 RCL X C058 STO K C059 RCL Y C060 STO L C061 RCL Z C062 STO M C063 XEQ C003 C064 RCL÷ T C065 STO U C066 "X=" C067 STOP C068 RCL A C069 STO K C070 RCL B C071 STO L C072 RCL C C073 STO M C074 RCL X C075 STO N C076 RCL Y C077 STO O C078 RCL Z C079 STO P C080 XEQ C003 C081 RCL÷ T C082 STO V C083 "Y=" C084 STOP C085 RCL D C086 STO N C087 RCL E C088 STO O C089 RCL F C090 STO P C091 RCL X C092 STO Q C093 RCL Y C094 STO R C095 RCL Z C096 STO S C097 XEQ C003 C098 RCL÷ T C099 STO W C100 "Z=" C101 CF 10 C102 TOP C103 RTN```

Examples:

[[ -3, 2, -4 ] [[ x ] = [[ 0 ]
[ 6, 1, 2 ] [ y ] = [ 2 ]
[ 3, 3, 7 ]] [ z ]] = [ 6 ]]
T: -135
x ≈ 0.0296
y ≈ 0.9333
z ≈ 0.4444

[[ 0, 10, 6 ] [[ x ] = [[ 3 ]
[ 5, 3, 8 ] [ y ] = [ 6.5 ]
[ -5, 8, 2 ]] [ z ]] = [ 7 ]]
T: -830
x ≈ -0.0843
y ≈ 0.6687
z ≈ 0.6145

Source:

Pike, Scott. "Using Cramer's Rule to Solve Three Equations with Three Unknowns" Mesa Community College. http://www.mesacc.edu/~scotz47781/mat150..._Notes.pdf Retrieved September 24, 2019
Reference URL's
• HP Forums: https://www.hpmuseum.org/forum/index.php
• :