## Saturday, November 9, 2019

### HP 35S: Determinant and Cramers Rule - 3 x 3 Matrices

HP 35S: Determinant and Cramers Rule - 3 x 3 Matrices

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

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

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/cramers_rule/Cramers_Rule_3_by_3_Notes.pdf  Retrieved September 24, 2019

Eddie

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