SIMEQN.xls

7/25/2019 SIMEQN.xls

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Solution of 2 Simultaneous Equations with 2 Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) = C1

Eqn. #2: a2*(X1) + b2*(X2) = C2

Input 2x2 Matrix Coefficients: Input Column Matrix Constants:a b C

1: 1.0000 2.0000 1: 4.0000

2: 3.0000 1.0000 2: 5.0000

1: 2:

2x2 Matrix Inverse:

1: -0.2000 0.4000

2: 0.6000 -0.2000

Results of 2x2 Solution:

X1 = 1.2000

X2 = 1.4000


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Solution of Simultaneous Equations with Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) = C1

Eqn. #2: a2*(X1) + b2*(X2) + c2*(X3) = C2

Eqn. #3: a3*(X1) + b3*(X2) + c3*(X3) = C3

Input x Matrix Coefficients: Input Column Matrix Constants:

a b c C

1: 3.0000 4.0000 0.0000 1: 8.0000

2: 4.0000 8.0000 1.0000 2: 1.0000

3: 5.0000 -1.0000 3.0000 3: 0.0000

1: 2: 3:

x Matrix Inverse:

1: 0.5319 -0.2553 0.0851

2: -0.1489 0.1915 -0.0638

3: -0.9362 0.4894 0.1702

Results of x Solution:X1 = 4.0000

X2 = -1.0000

X3 = -7.0000


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Solution of ! Simultaneous Equations with ! Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) + d1*(X4) = C1

Eqn. #2: a2*(X1) + b2*(X2) + c2*(X3) + d2*(X4) = C2

Eqn. #3: a3*(X1) + b3*(X2) + c3*(X3) + d3*(X4) = C3

Eqn. #4: a4*(X1) + b4*(X2) + c4*(X3) + d4*(X4) = C4

Input !x! Matrix Coefficients: Input Column Matrix Constants:

a b c d C

1: 2.0000 -1.0000 0.0000 0.0000 1: 34.0000

2: -1.0000 3.0000 -1.0000 0.0000 2: 0.0000

3: 0.0000 -1.0000 3.0000 -1.0000 3: 0.0000

4: 0.0000 0.0000 -1.0000 3.0000 4: 0.0000

1: 2: 3: 4:

!x! Matrix Inverse:

1: 0.6176 0.2353 0.0882 0.0294

2: 0.2353 0.4706 0.1765 0.0588

3: 0.0882 0.1765 0.4412 0.1471

4: 0.0294 0.0588 0.1471 0.3824

Results of !x! Solution:

X1 = 21.0000

X2 = 8.0000

X3 = 3.0000

X4 = 1.0000


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Solution of " Simultaneous Equations with " Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) + d1*(X4) + e1*(X5) = C1

Eqn. #2: a2*(X1) + b2*(X2) + c2*(X3) + d2*(X4) + e2*(X5) = C2

Eqn. #3: a3*(X1) + b3*(X2) + c3*(X3) + d3*(X4) + e3*(X5) = C3

Eqn. #4: a4*(X1) + b4*(X2) + c4*(X3) + d4*(X4) + e4*(X5) = C4Eqn. #5: a5*(X1) + b5*(X2) + c5*(X3) + d5*(X4) + e5*(X5) = C5

Input "x" Matrix Coefficients: Input Column Matrix Constants:

a b c d e C

1: 20000.0000 0.0029 0.0000 0.0000 0.0000 1: -0.2903

2: 0.0029 0.0116 0.0029 0.0000 0.0000 2: -0.5806

3: 0.0000 0.0029 0.0116 0.0029 0.0000 3: -0.5806

4: 0.0000 0.0000 0.0029 0.0116 0.0029 4: -0.5806

5: 0.0000 0.0000 0.0000 0.0029 0.0116 5: -0.2903

1: 2: 3: 4: 5:

"x" Matrix Inverse:

1: 0.0001 0.0000 0.0000 0.0000 0.0000

2: 0.0000 92.3062 -24.7249 6.5933 -1.6483

3: 0.0000 -24.7249 98.8995 -26.3732 6.5933

4: 0.0000 6.5933 -26.3732 98.8995 -24.7249

5: 0.0000 -1.6483 6.5933 -24.7249 92.3062

Results of "x" Solution:

X1 = 0.0000

X2 = -42.5837

X3 = -29.6651

X4 = -38.7560

X5 = -15.3110


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Solution of # Simultaneous Equations with # Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) + d1*(X4) + e1*(X5) + f1*(X6) = C1



Eqn. #4: a4*(X1) + b4*(X2) + c4*(X3) + d4*(X4) + e4*(X5) + f4*(X6) = C4Eqn. #5: a5*(X1) + b5*(X2) + c5*(X3) + d5*(X4) + e5*(X5) + f5*(X6) = C5


Input #x# Matrix Coefficients: Input Column Matrix Constants:

a b c d e f C

1: 1153.4465 83.0940 5085.9713 -1087.1724 -83.0940 -83.4074 1: 3.2500

2: 83.0940 3731.2912 1084.2968 -83.0940 -13.3425 1084.2968 2: -13.0384

3: 5085.9713 1084.2968 764483.6283 83.4074 -1084.2968 113434.1219 3: -677.9971

4: -1087.1724 -83.0940 83.4074 1130.3144 83.0940 3966.1852 4: 0.0000

5: -83.0940 -13.3425 -1084.2968 83.0940 3235.5647 -1084.2968 5: -13.0384

6: -83.4074 1084.2968 113434.1219 3966.1852 -1084.2968 692801.5770 6: 677.9971

1: 2: 3: 4: 5: 6:

#x# Matrix Inverse:

1: 0.0168 0.0000 -0.0001 0.0164 -0.0001 -0.0001

2: 0.0000 0.0003 0.0000 0.0001 0.0000 0.0000

3: -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000

4: 0.0164 0.0001 -0.0001 0.0170 -0.0001 -0.0001

5: -0.0001 0.0000 0.0000 -0.0001 0.0003 0.0000

6: -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000

Results of #x# Solution:

X1 = 0.0730

X2 = -0.0034

X3 = -0.0015

X4 = 0.0674

X5 = -0.0041

X6 = 0.0008


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Solution of $ Simultaneous Equations with $ Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) + d1*(X4) + e1*(X5) + f1*(X6) + 1*(X7) = C1



Eqn. #4: a4*(X1) + b4*(X2) + c4*(X3) + d4*(X4) + e4*(X5) + f4*(X6) + 4*(X7) = C4Eqn. #5: a5*(X1) + b5*(X2) + c5*(X3) + d5*(X4) + e5*(X5) + f5*(X6) + 5*(X7) = C5



Input $x$ Matrix Coefficients: Input Col% Matrix Con

a b c d e f C

1: 1153.4465 83.0940 5085.9713 -1087.1724 -83.0940 -83.4074 0.0000 1: 3.2500

2: 83.0940 3731.2912 1084.2968 -83.0940 -13.3425 1084.2968 0.0000 2: -13.0384

3: 5085.9713 1084.2968 764483.6283 83.4074 -1084.2968 113434.1219 0.0000 3: -677.9971

4: -1087.1724 -83.0940 83.4074 1130.3144 83.0940 3966.1852 3882.7778 4: 0.0000

5: -83.0940 -13.3425 -1084.2968 83.0940 3235.5647 -1084.2968 0.0000 5: -13.0384

6: -83.4074 1084.2968 113434.1219 3966.1852 -1084.2968 692801.5770 232966.6667 6: 677.9971

7: 0.0000 0.0000 0.0000 3882.7778 0.0000 232966.6667 465933.3333 7: 0.00001: 2: 3: 4: 5: 6: 7:

$x$ Matrix Inverse:

1: 0.0253 0.0001 -0.0002 0.0251 -0.0001 -0.0001 -0.0002

2: 0.0001 0.0003 0.0000 0.0001 0.0000 0.0000 0.0000

3: -0.0002 0.0000 0.0000 -0.0002 0.0000 0.0000 0.0000

4: 0.0251 0.0001 -0.0002 0.0259 -0.0001 -0.0001 -0.0002

5: -0.0001 0.0000 0.0000 -0.0001 0.0003 0.0000 0.0000

6: -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000 0.0000

7: 0.0253 0.0000 0.0000 -0.0002 0.0000 0.0000 0.0000

Results of $x$ Solution:

X1 = 0.1572

X2 = -0.0033

X3 = -0.0021

X4 = 0.1539

X5 = -0.0043

X6 = 0.0011

X7 = 0.0809


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Solution of & Simultaneous Equations with & Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) + d1*(X4) + e1*(X5) + f1*(X6) + 1*(X7) + !1*(X8) =








Input &x& Matrix Coefficients: Input C

a b c d e f !

1: 1153.4465 83.0940 5085.9713 -1087.1724 -83.0940 -83.4074 5169.3787 0.0000 1:

2: 83.0940 3731.2912 1084.2968 -83.0940 -13.3425 1084.2968 0.0000 0.0000 2:

3: 5085.9713 1084.2968 764483.6283 83.4074 -1084.2968 113434.1219 268807.6923 0.0000 3:

4: -1087.1724 -83.0940 83.4074 1130.3144 83.0940 3966.1852 0.0000 3882.7778 4:

5: -83.0940 -13.3425 -1084.2968 83.0940 3235.5647 -1084.2968 0.0000 0.0000 5:

6: -83.4074 1084.2968 113434.1219 3966.1852 -1084.2968 692801.5770 0.0000 232966.6667 6:

7: 5169.3787 0.0000 268807.6923 0.0000 0.0000 0.0000 537615.3846 0.0000 7:

8: 0.0000 0.0000 0.0000 3882.7778 0.0000 232966.6667 0.0000 465933.3333 8:

1: 2: 3: 4: 5: 6: 7: 8:

&x& Matrix Inverse:

1: 0.0782 0.0001 -0.0003 0.0779 -0.0002 -0.0002 -0.0006 -0.0005

2: 0.0001 0.0003 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000

3: -0.0003 0.0000 0.0000 -0.0003 0.0000 0.0000 0.0000 0.0000

4: 0.0779 0.0002 -0.0003 0.0785 -0.0002 -0.0002 -0.0006 -0.0005

5: -0.0002 0.0000 0.0000 -0.0002 0.0003 0.0000 0.0000 0.0000

6: -0.0002 0.0000 0.0000 -0.0002 0.0000 0.0000 0.0000 0.0000

7: -0.0006 0.0000 0.0000 -0.0006 0.0000 0.0000 0.0000 0.0000

8: -0.0005 0.0000 0.0000 -0.0005 0.0000 0.0000 0.0000 0.0000

Results of &x& Solution:

X1 = 0.3068

X2 = -0.0031

X3 = -0.0025

X4 = 0.3029

X5 = -0.0046

X6 = 0.0006

X7 = -0.0017

X8 = -0.0028


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Solution of ' Simultaneous Equations with ' Unknowns:

Format:

Eqn. #1: a1*(X1) + b1*(X2) + c1*(X3) + d1*(X4) + e1*(X5) + f1*(X6) + 1*(X7) + !1*(X8) + "1*(X9)


Eqn. #3: a3*(X1) + b3*(X2) + c3*(X3) + d3*(X4) + e3*(X5) + f3*(X6) + 3*(X7) + !3*(X8) + "3*(X9) Eqn. #4: a4*(X1) + b4*(X2) + c4*(X3) + d4*(X4) + e4*(X5) + f4*(X6) + 4*(X7) + !4*(X8) + "4*(X9)






Input 'x' Matrix Coefficients:

a b c d e f ! "

1: 2185.4794 317.6985 4519.4002 -2119.2053 -317.6985 -649.9785 0.0000 0.0000 0.0000

2: 317.6985 3820.9903 4224.8605 -317.6985 -103.0416 4224.8605 0.0000 0.0000 0.0000

3: 4519.4002 4224.8605 987400.5356 649.9785 -4224.8605 224892.5755 0.0000 0.0000 0.0000

4: -2119.2053 -317.6985 649.9785 4238.4106 0.0000 1299.9571 -2119.2053 317.6985 649.9785

5: -317.6985 -103.0416 -4224.8605 0.0000 206.0832 0.0000 317.6985 -103.0416 4224.8605

6: -649.9785 4224.8605 224892.5755 1299.9571 0.0000 899570.3020 -649.9785 -4224.8605 224892.575

7: 0.0000 0.0000 0.0000 -2119.2053 317.6985 -649.9785 2185.4794 -317.6985 4519.4002

8: 0.0000 0.0000 0.0000 317.6985 -103.0416 -4224.8605 -317.6985 3820.9903 -4224.8605

9: 0.0000 0.0000 0.0000 649.9785 4224.8605 224892.5755 4519.4002 -4224.8605 987400.535

1: 2: 3: 4: 5: 6: 7: 8: 9:

'x' Matrix Inverse:

1: 0.0145 0.0000 -0.0001 0.0140 0.0016 0.0000 0.0136 0.0000 -0.0001

2: 0.0000 0.0003 0.0000 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000

3: -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000

4: 0.0140 0.0001 -0.0001 0.0143 0.0000 0.0000 0.0140 -0.0001 -0.0001

5: 0.0016 0.0001 0.0000 0.0000 0.0115 0.0000 -0.0016 0.0001 0.0000

6: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

7: 0.0136 0.0000 -0.0001 0.0140 -0.0016 0.0000 0.0145 0.0000 -0.0001

8: 0.0000 0.0000 0.0000 -0.0001 0.0001 0.0000 0.0000 0.0003 0.0000

9: -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000

Results of 'x' Solution:

X1 = 0.0247

X2 = -0.0034

X3 = -0.0010

X4 = 0.0456

X5 = -0.1627

X6 = 0.0001

X7 = 0.0664

X8 = -0.0037X9 = 0.0005


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onstants:


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Solution of () Simultaneous Equations with () Unknowns:

Format:


Eqn. #2: a2*(X1) + b2*(X2) + c2*(X3) + d2*(X4) + e2*(X5) + f2*(X6) + 2*(X7) + !2*(X8) + "2*(X9)Eqn. #3: a3*(X1) + b3*(X2) + c3*(X3) + d3*(X4) + e3*(X5) + f3*(X6) + 3*(X7) + !3*(X8) + "3*(X9)







Eqn. #10: a10*(X1) + b10*(X2) + c10*(X3) + d10*(X4) + e10*(X5) + f10*(X6) + 10*(X7) + !10*(X8) + "10*(X9

Input ()x() Matrix Coefficients:

a b c d e f ! "

1: 2185.4794 317.6985 4519.4002 -2119.2053 -317.6985 -649.9785 0.0000 0.0000 0.0000

2: 317.6985 3820.9903 4224.8605 -317.6985 -103.0416 4224.8605 0.0000 0.0000 0.00003: 4519.4002 4224.8605 987400.5356 649.9785 -4224.8605 224892.5755 0.0000 0.0000 0.0000

4: -2119.2053 -317.6985 649.9785 4238.4106 0.0000 1299.9571 -2119.2053 317.6985 649.978

5: -317.6985 -103.0416 -4224.8605 0.0000 206.0832 0.0000 317.6985 -103.0416 4224.860

6: -649.9785 4224.8605 224892.5755 1299.9571 0.0000 899570.3020 -649.9785 -4224.8605 224892.57

7: 0.0000 0.0000 0.0000 -2119.2053 317.6985 -649.9785 2185.4794 -317.6985 4519.400

8: 0.0000 0.0000 0.0000 317.6985 -103.0416 -4224.8605 -317.6985 3820.9903 -4224.86

9: 0.0000 0.0000 0.0000 649.9785 4224.8605 224892.5755 4519.4002 -4224.8605 987400.53

10: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 5169.3787 0.0000 268807.69

1: 2: 3: 4: 5: 6: 7: 8: 9:

()x() Matrix Inverse:

1: 0.0233 0.0001 -0.0001 0.0236 -0.0021 0.0001 0.0238 -0.0001 -0.0001

2: 0.0001 0.0003 0.0000 0.0001 0.0001 0.0000 0.0001 0.0000 0.0000

3: -0.0001 0.0000 0.0000 -0.0002 0.0001 0.0000 -0.0002 0.0000 0.0000

4: 0.0236 0.0001 -0.0002 0.0246 -0.0040 0.0001 0.0251 -0.0001 -0.0001

5: -0.0021 0.0001 0.0001 -0.0040 0.0131 0.0000 -0.0058 0.0001 0.0000

6: 0.0001 0.0000 0.0000 0.0001 0.0000 0.0000 0.0001 0.0000 0.0000

7: 0.0238 0.0001 -0.0002 0.0251 -0.0058 0.0001 0.0263 -0.0001 -0.0001

8: -0.0001 0.0000 0.0000 -0.0001 0.0001 0.0000 -0.0001 0.0003 0.0000

9: -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000 -0.0001 0.0000 0.0000

10: -0.0002 0.0000 0.0000 -0.0002 0.0001 0.0000 -0.0002 0.0000 0.0000

Results of ()x() Solution:

X1 = 0.1153

X2 = -0.0032

X3 = -0.0017

X4 = 0.1432

X5 = -0.2002

X6 = 0.0003

X7 = 0.1708

X8 = -0.0039

X9 = 0.0006

X10 = -0.0019


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SIMEQN.xls

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