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PERSAMAAN CREMER
PERSAMAAN MATRIK:
NO.1 :
X1 X2 X3 X4 b
1 2 3 1 2 11
2 3 4 2 6 12
3 2 5 1 2 13
4 4 2 2 2 -14
SOLUTION:
MATRIX 1 ( A)
Sign A1 A2 A3 A4
+
1 2 3 1 2
2 3 4 2 6
3 2 5 1 2
4 4 2 2 2
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Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4
+
1 2 3 1 2
2 0 -0.5 0.5 3
3 0 2 0 0
4 0 -4 0 -2
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4
+
1 2 3 1 2
2 0 -0.5 0.5 3
3 0 0 2 12
4 0 0 -4 -26
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4
+
1 2 3 1 2
2 0 -0.5 0.5 3
3 0 0 2 12
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4 0 0 0 -2
Multiply the main diagonal elements
Sign A1 A2 A3 A4
+
1 2 3 1 2
2 0 -0.5 0.5 3
3 0 0 2 12
4 0 0 0 -2
2 x (-0.5) x 2 x (-2) = 4
Result:
Determinant is 4
MATRIX 2 ( B)
Sign A1 A2 A3 A4
+
1 11 3 1 2
2 12 4 2 6
3 13 5 1 2
4 -14 2 2 2
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Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4
+
1 11 3 1 2
2 0 0.7272727272727275 0.9090909090909092 3.8181818181818183
3 0 1.454545454545455 -0.18181818181818188 -0.36363636363636376
4 0 5.818181818181818 3.2727272727272725 4.545454545454545
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4
+
1 11 3 1 2
2 0 0.7272727272727275 0.9090909090909092 3.8181818181818183
3 0 0 -2.0000000000000004 -8
4 0 0 -3.999999999999999 -25.999999999999993
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4
+
1 11 3 1 2
2 0 0.7272727272727275 0.9090909090909092 3.8181818181818183
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3 0 0 -2.0000000000000004 -8
4 0 0 0 -10
Multiply the main diagonal elements
Sign A1 A2 A3 A4
+
1 11 3 1 2
2 0 0.7272727272727275 0.9090909090909092 3.8181818181818183
3 0 0 -2.0000000000000004 -8
4 0 0 0 -10
11 x 0.7272727272727275 x (-2.0000000000000004) x (-10) = 160.0000000000001
Result:
Determinant is 160.0000000000001
MATRIX 3 ( C)
Sign A1 A2 A3 A4
+
1 2 11 1 2
2 3 12 2 6
3 2 13 1 2
4 4 -14 2 2
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Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4
+
1 2 11 1 2
2 0 -4.5 0.5 3
3 0 2 0 0
4 0 -36 0 -2
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4
+
1 2 11 1 2
2 0 -4.5 0.5 3
3 0 0 0.2222222222222222 1.3333333333333333
4 0 0 -4 -26
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4
+
1 2 11 1 2
2 0 -4.5 0.5 3
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3 0 0 0.2222222222222222 1.3333333333333333
4 0 0 0 -2
Multiply the main diagonal elements
Sign A1 A2 A3 A4
+
1 2 11 1 2
2 0 -4.5 0.5 3
3 0 0 0.2222222222222222 1.3333333333333333
4 0 0 0 -2
2 x (-4.5) x 0.2222222222222222 x (-2) = 4
Result:
Determinant is 4
MATRIX 4 ( D)
Sign A1 A2 A3 A4
+
1 2 3 11 2
2 3 4 12 6
3 2 5 13 2
4 4 2 -14 2
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Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4
+
1 2 3 11 2
2 0 -0.5 -4.5 3
3 0 2 2 0
4 0 -4 -36 -2
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4
+
1 2 3 11 2
2 0 -0.5 -4.5 3
3 0 0 -16 12
4 0 0 0 -26
Multiply the main diagonal elements
Sign A1 A2 A3 A4
+
1 2 3 11 2
2 0 -0.5 -4.5 3
3 0 0 -16 12
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4 0 0 0 -26
2 x (-0.5) x (-16) x (-26) = -416
Result:
Determinant is -416
MATRIX 5 ( E)
Sign A1 A2 A3 A4
+
1 2 3 1 11
2 3 4 2 12
3 2 5 1 13
4 4 2 2 -14
Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4
+
1 2 3 1 11
2 0 -0.5 0.5 -4.5
3 0 2 0 2
4 0 -4 0 -36
Eliminate elements in the 2nd column under the 2nd element
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Sign A1 A2 A3 A4
+
1 2 3 1 11
2 0 -0.5 0.5 -4.5
3 0 0 2 -16
4 0 0 -4 0
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4
+
1 2 3 1 11
2 0 -0.5 0.5 -4.5
3 0 0 2 -16
4 0 0 0 -32
Multiply the main diagonal elements
Sign A1 A2 A3 A4
+
1 2 3 1 11
2 0 -0.5 0.5 -4.5
3 0 0 2 -16
4 0 0 0 -32
2 x (-0.5) x 2 x (-32) = 64
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Result:
Determinant is 64
JAWABAN :
X1 = B / D = 160.0000000000001 / 4 = 40.00000000000003
X2 = C / D = 4 / 4 = 1
X3 = D / D = -416 / 4 = -104
X4 = D4 / D = 64 / 4 = 16
SOLUTION SET:
X1 = 40.00000000000003
X2 = 1
X3 = -104
X4 = 16
NO.2 :
X1 X2 X3 X4 X5 b
1 1 2 3 4 5 14
2 1 2 5 1 2 15
3 2 5 1 2 1 16
4 4 2 2 6 3 17
5 2 4 1 6 1 18
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SOLUTION:
MATRIX 1 ( A)
Sign A1 A2 A3 A4 A5
+
1 1 2 3 4 5
2 1 2 5 1 2
3 2 5 1 2 1
4 4 2 2 6 3
5 2 4 1 6 1
Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4 A5
+
1 1 2 3 4 5
2 0 0 2 -3 -3
3 0 1 -5 -6 -9
4 0 -6 -10 -10 -17
5 0 0 -5 -2 -9
Swap the 2nd and the 3rd rows inversing determinant sign
Sign A1 A2 A3 A4 A5
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-
1 1 2 3 4 5
2 0 1 -5 -6 -9
3 0 0 2 -3 -3
4 0 -6 -10 -10 -17
5 0 0 -5 -2 -9
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 5
2 0 1 -5 -6 -9
3 0 0 2 -3 -3
4 0 0 -40 -46 -71
5 0 0 -5 -2 -9
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 5
2 0 1 -5 -6 -9
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3 0 0 2 -3 -3
4 0 0 0 -106 -131
5 0 0 0 -9.5 -16.5
Eliminate elements in the 4th column under the 4th element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 5
2 0 1 -5 -6 -9
3 0 0 2 -3 -3
4 0 0 0 -106 -131
5 0 0 0 0 -4.759433962264151
Multiply the main diagonal elements
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 5
2 0 1 -5 -6 -9
3 0 0 2 -3 -3
4 0 0 0 -106 -131
5 0 0 0 0 -4.759433962264151
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-(1 x 1 x 2 x (-106) x (-4.759433962264151)) = -1008.9999999999999
Result:
Determinant is -1008.9999999999999
MATRIX 2 ( B)
Sign A1 A2 A3 A4 A5
+
1 14 2 3 4 5
2 15 2 5 1 2
3 16 5 1 2 1
4 17 2 2 6 3
5 18 4 1 6 1
Eliminate elements in the 1st column under the 1st element
Sig
n A1 A2 A3 A4 A5
+
1 14 2 3 4 5
2 0
-
0.14285714285
71428
1.7857142857142
86
-
3.2857142857
142856
-
3.35714285714
28577
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3 02.71428571428
57144
-
2.4285714285714
284
-
2.5714285714
28571
-
4.71428571428
5714
4 0
-
0.42857142857
14284
-
1.6428571428571
428
1.1428571428
571432
-
3.07142857142
8571
5 01.42857142857
14288
-
2.8571428571428
568
0.8571428571
428577
-
5.42857142857
1429
Eliminate elements in the 2nd column under the 2nd element
Sig
n
A
1A2 A3 A4 A5
+
11
42 3 4 5
2 0
-
0.142857142857
1428
1.785714285714
286
-
3.285714285714
2856
-
3.357142857142
8577
3 0 031.50000000000
0025
-
65.00000000000
003
-
68.50000000000
004
4 0 0 -7 117.000000000000
002
5 0 0 15.00000000000 - -
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Sig
n
A
1A2 A3 A4 A5
+
11
42 3 4 5
2 0
-
0.142857142857
1428
1.785714285714
286
-
3.285714285714
2856
-
3.357142857142
8577
3 0 0
31.50000000000
0025
-
65.00000000000003
-
68.50000000000004
4 0 0 0
-
3.444444444444
4393
-
8.222222222222
22
5 0 0 0 0
-
3.8801843317972398
Multiply the main diagonal elements
Sig
n
A
1A2 A3 A4 A5
+
11
42 3 4 5
2 0-
0.142857142857
1.785714285714
286
-
3.285714285714
-
3.357142857142
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1428 2856 8577
3 0 031.50000000000
0025
-
65.00000000000
003
-
68.50000000000
004
4 0 0 0
-
3.444444444444
4393
-
8.222222222222
22
5 0 0 0 0
-
3.8801843317972398
14 x (-0.1428571428571428) x 31.500000000000025 x (-3.4444444444444393) x (-
3.8801843317972398) = -842
Result:
Determinant is -842
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 1 15 5 1 2
3 2 16 1 2 1
4 4 17 2 6 3
5 2 18 1 6 1
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Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 -12 -5 -6 -9
4 0 -39 -10 -10 -17
5 0 -10 -5 -2 -9
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 68 -127 -134
5 0 0 15 -32 -39
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4 A5
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+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 0 23.31578947368422 27.05263157894734
5 0 0 0 1.1578947368421098 -3.473684210526315
Eliminate elements in the 4th column under the 4th element
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 0 23.31578947368422 27.05263157894734
5 0 0 0 0 -4.817155756207677
Multiply the main diagonal elements
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
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4 0 0 0 23.31578947368422 27.05263157894734
5 0 0 0 0 -4.817155756207677
1 x 1 x 19 x 23.31578947368422 x (-4.817155756207677) = -2134.000000000002
MATRIX 3 ( C)
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 1 15 5 1 2
3 2 16 1 2 1
4 4 17 2 6 3
5 2 18 1 6 1
Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 -12 -5 -6 -9
4 0 -39 -10 -10 -17
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5 0 -10 -5 -2 -9
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 68 -127 -134
5 0 0 15 -32 -39
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 0 23.31578947368422 27.05263157894734
5 0 0 0 1.1578947368421098 -3.473684210526315
Eliminate elements in the 4th column under the 4th element
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Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 0 23.31578947368422 27.05263157894734
5 0 0 0 0 -4.817155756207677
Multiply the main diagonal elements
Sign A1 A2 A3 A4 A5
+
1 1 14 3 4 5
2 0 1 2 -3 -3
3 0 0 19 -42 -45
4 0 0 0 23.31578947368422 27.05263157894734
5 0 0 0 0 -4.817155756207677
1 x 1 x 19 x 23.31578947368422 x (-4.817155756207677) = -2134.000000000002
Result:
Determinant is -2134.000000000002
MATRIX 4 ( D)
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Sign A1 A2 A3 A4 A5
+
1 1 2 14 4 5
2 1 2 15 1 2
3 2 5 16 2 1
4 4 2 17 6 3
5 2 4 18 6 1
Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4 A5
+
1 1 2 14 4 5
2 0 0 1 -3 -3
3 0 1 -12 -6 -9
4 0 -6 -39 -10 -17
5 0 0 -10 -2 -9
Swap the 2nd and the 3rd rows inversing determinant sign
Sign A1 A2 A3 A4 A5
-
1 1 2 14 4 5
2 0 1 -12 -6 -9
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3 0 0 1 -3 -3
4 0 -6 -39 -10 -17
5 0 0 -10 -2 -9
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4 A5
-
1 1 2 14 4 5
2 0 1 -12 -6 -9
3 0 0 1 -3 -3
4 0 0 -111 -46 -71
5 0 0 -10 -2 -9
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4 A5
-
1 1 2 14 4 5
2 0 1 -12 -6 -9
3 0 0 1 -3 -3
4 0 0 0 -379 -404
5 0 0 0 -32 -39
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Eliminate elements in the 4th column under the 4th element
Sign A1 A2 A3 A4 A5
-
1 1 2 14 4 5
2 0 1 -12 -6 -9
3 0 0 1 -3 -3
4 0 0 0 -379 -404
5 0 0 0 0 -4.889182058047496
Multiply the main diagonal elements
Sign A1 A2 A3 A4 A5
-
1 1 2 14 4 5
2 0 1 -12 -6 -9
3 0 0 1 -3 -3
4 0 0 0 -379 -404
5 0 0 0 0 -4.889182058047496
-(1 x 1 x 1 x (-379) x (-4.889182058047496)) = -1853.000000000001
Result:
Determinant is -1853.000000000001
MATRIX 5 ( E)
Your matrix
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Sign A1 A2 A3 A4 A5
+
1 1 2 3 14 5
2 1 2 5 15 2
3 2 5 1 16 1
4 4 2 2 17 3
5 2 4 1 18 1
Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4 A5
+
1 1 2 3 14 5
2 0 0 2 1 -3
3 0 1 -5 -12 -9
4 0 -6 -10 -39 -17
5 0 0 -5 -10 -9
Swap the 2nd and the 3rd rows inversing determinant sign
Sign A1 A2 A3 A4 A5
-
1 1 2 3 14 5
2 0 1 -5 -12 -9
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3 0 0 2 1 -3
4 0 -6 -10 -39 -17
5 0 0 -5 -10 -9
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 14 5
2 0 1 -5 -12 -9
3 0 0 2 1 -3
4 0 0 -40 -111 -71
5 0 0 -5 -10 -9
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 14 5
2 0 1 -5 -12 -9
3 0 0 2 1 -3
4 0 0 0 -91 -131
5 0 0 0 -7.5 -16.5
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Eliminate elements in the 4th column under the 4th element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 14 5
2 0 1 -5 -12 -9
3 0 0 2 1 -3
4 0 0 0 -91 -131
5 0 0 0 0 -5.703296703296703
Multiply the main diagonal elements
Sign A1 A2 A3 A4 A5
-
1 1 2 3 14 5
2 0 1 -5 -12 -9
3 0 0 2 1 -3
4 0 0 0 -91 -131
5 0 0 0 0 -5.703296703296703
-(1 x 1 x 2 x (-91) x (-5.703296703296703)) = -1037.9999999999998
Result:
Determinant is -1037.9999999999998
MATRIX 6 ( E)
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Sign A1 A2 A3 A4 A5
+
1 1 2 3 4 14
2 1 2 5 1 15
3 2 5 1 2 16
4 4 2 2 6 17
5 2 4 1 6 18
Eliminate elements in the 1st column under the 1st element
Sign A1 A2 A3 A4 A5
+
1 1 2 3 4 14
2 0 0 2 -3 1
3 0 1 -5 -6 -12
4 0 -6 -10 -10 -39
5 0 0 -5 -2 -10
Swap the 2nd and the 3rd rows inversing determinant sign
Sign A1 A2 A3 A4 A5
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-
1 1 2 3 4 14
2 0 1 -5 -6 -12
3 0 0 2 -3 1
4 0 -6 -10 -10 -39
5 0 0 -5 -2 -10
Eliminate elements in the 2nd column under the 2nd element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 14
2 0 1 -5 -6 -12
3 0 0 2 -3 1
4 0 0 -40 -46 -111
5 0 0 -5 -2 -10
Eliminate elements in the 3rd column under the 3rd element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 14
2 0 1 -5 -6 -12
3 0 0 2 -3 1
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4 0 0 0 -106 -91
5 0 0 0 -9.5 -7.5
Eliminate elements in the 4th column under the 4th element
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 14
2 0 1 -5 -6 -12
3 0 0 2 -3 1
4 0 0 0 -106 -91
5 0 0 0 0 0.6556603773584904
Multiply the main diagonal elements
Sign A1 A2 A3 A4 A5
-
1 1 2 3 4 14
2 0 1 -5 -6 -12
3 0 0 2 -3 1
4 0 0 0 -106 -91
5 0 0 0 0 0.6556603773584904
-(1 x 1 x 2 x (-106) x 0.6556603773584904) = 138.99999999999994
Result:
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Determinant is 138.99999999999994
x1 = D1 / D = -842 / (-1008.9999999999999) = 0.8344895936570863
x2 = D2 / D = -2134.000000000002 / (-1008.9999999999999) = 2.1149653121902894
x3 = D3 / D = -1853.000000000001 / (-1008.9999999999999) = 1.8364717542120923
x4 = D4 / D = -1037.9999999999998 / (-1008.9999999999999) = 1.0287413280475717
x5 = D5 / D = 138.99999999999994 / (-1008.9999999999999) = -0.13776015857284435
Solution set:
x1 = 0.8344895936570863
x2 = 2.1149653121902894
x3 = 1.8364717542120923
x4 = 1.0287413280475717
x5 = -0.13776015857284435
PERSAMAAN GAUSS-JORDAN
ORDE 4 X 4
X1 X2 X3 X4 b
1 1 2 3 4 2
2 4 5 2 2 3
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3 2 7 4 5 4
4 3 2 5 2 5
5 4 2 4 4 6
Find the pivot in the 1st column in the 1st row
X1 X2 X3 X4 b
1 1 2 3 4 2
2 4 5 2 2 3
3 2 7 4 5 4
4 3 2 5 2 5
5 4 2 4 4 6
Eliminate the 1st column
X1 X2 X3 X4 b
1 1 2 3 4 2
2 0 -3 -10 -14 -5
3 0 3 -2 -3 0
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4 0 -4 -4 -10 -1
5 0 -6 -8 -12 -2
Make the pivot in the 2nd column by dividing the 2nd row by -3
X1 X2 X3 X4 b
1 1 2 3 4 2
2 0 1 10/3 14/3 5/3
3 0 3 -2 -3 0
4 0 -4 -4 -10 -1
5 0 -6 -8 -12 -2
Eliminate the 2nd column
X1 X2 X3 X4 b
1 1 0 -11/3 -16/3 -4/3
2 0 1 10/3 14/3 5/3
3 0 0 -12 -17 -5
4 0 0 28/3 26/3 17/3
5 0 0 12 16 8
Make the pivot in the 3rd column by dividing the 3rd row by -12
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X1 X2 X3 X4 b
1 1 0 -11/3 -16/3 -4/3
2 0 1 10/3 14/3 5/3
3 0 0 1 17/12 5/12
4 0 0 28/3 26/3 17/3
5 0 0 12 16 8
Eliminate the 3rd column
X1 X2 X3 X4 b
1 1 0 0 -5/36 7/36
2 0 1 0 -1/18 5/18
3 0 0 1 17/12 5/12
4 0 0 0 -41/9 16/9
5 0 0 0 -1 3
Find the pivot in the 4th column (inversing the sign in the whole row) and swap the 5th and the
4th rows
X1 X2 X3 X4 b
1 1 0 0 -5/36 7/36
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2 0 1 0 -1/18 5/18
3 0 0 1 17/12 5/12
4 0 0 0 1 -3
5 0 0 0 -41/9 16/9
Eliminate the 4th column
X1 X2 X3 X4 b
1 1 0 0 0 -2/9
2 0 1 0 0 1/9
3 0 0 1 0 14/3
4 0 0 0 1 -3
5 0 0 0 0 -107/9
A= -2/9
B= 1/9
C= 14/3
D= -3
E= -107/9
ORDE 5 X 5
X1 X2 X3 X4 X5 b
8/12/2019 Persamaan Cremeeer
39/44
1 2 3 2 2 2 2
2 3 3 2 7 2 5
3 4 2 3 2 4 3
4 5 3 4 2 4 5
5 6 4 2 3 2 6
6 7 2 3 3 2 2
Make the pivot in the 1st column by dividing the 1st row by 2
X1 X2 X3 X4 X5 b
1 1 3/2 1 1 1 1
2 3 3 2 7 2 5
3 4 2 3 2 4 3
4 5 3 4 2 4 5
5 6 4 2 3 2 6
6 7 2 3 3 2 2
Eliminate the 1st column
X1 X2 X3 X4 X5 b
1 1 3/2 1 1 1 1
8/12/2019 Persamaan Cremeeer
40/44
2 0 -3/2 -1 4 -1 2
3 0 -4 -1 -2 0 -1
4 0 -9/2 -1 -3 -1 0
5 0 -5 -4 -3 -4 0
6 0 -17/2 -4 -4 -5 -5
Make the pivot in the 2nd column by dividing the 2nd row by -3/2
X1 X2 X3 X4 X5 b
1 1 3/2 1 1 1 1
2 0 1 2/3 -8/3 2/3 -4/3
3 0 -4 -1 -2 0 -1
4 0 -9/2 -1 -3 -1 0
5 0 -5 -4 -3 -4 0
6 0 -17/2 -4 -4 -5 -5
Eliminate the 2nd column
X1 X2 X3 X4 X5 b
1 1 0 0 5 0 3
2 0 1 2/3 -8/3 2/3 -4/3
8/12/2019 Persamaan Cremeeer
41/44
3 0 0 5/3 -38/3 8/3 -19/3
4 0 0 2 -15 2 -6
5 0 0 -2/3 -49/3 -2/3 -20/3
6 0 0 5/3 -80/3 2/3 -49/3
Make the pivot in the 3rd column by dividing the 3rd row by 5/3
X1 X2 X3 X4 X5 b
1 1 0 0 5 0 3
2 0 1 2/3 -8/3 2/3 -4/3
3 0 0 1 -38/5 8/5 -19/5
4 0 0 2 -15 2 -6
5 0 0 -2/3 -49/3 -2/3 -20/3
6 0 0 5/3 -80/3 2/3 -49/3
Eliminate the 3rd column
X1 X2 X3 X4 X5 b
1 1 0 0 5 0 3
2 0 1 0 12/5 -2/5 6/5
3 0 0 1 -38/5 8/5 -19/5
8/12/2019 Persamaan Cremeeer
42/44
4 0 0 0 1/5 -6/5 8/5
5 0 0 0 -107/5 2/5 -46/5
6 0 0 0 -14 -2 -10
Make the pivot in the 4th column by dividing the 4th row by 1/5
X1 X2 X3 X4 X5 b
1 1 0 0 5 0 3
2 0 1 0 12/5 -2/5 6/5
3 0 0 1 -38/5 8/5 -19/5
4 0 0 0 1 -6 8
5 0 0 0 -107/5 2/5 -46/5
6 0 0 0 -14 -2 -10
Eliminate the 4th column
X1 X2 X3 X4 X5 b
1 1 0 0 0 30 -37
2 0 1 0 0 14 -18
3 0 0 1 0 -44 57
4 0 0 0 1 -6 8
8/12/2019 Persamaan Cremeeer
43/44
8/12/2019 Persamaan Cremeeer
44/44
6 0 0 0 0 0 -219/32
Dari operasi matematika diatas diperoleh nilai:
A= -9/32
B= 21/16
C= 13/32
D= -81/64
E= -219/32