tugas matrek gauss backward dan forward

8/18/2019 Tugas Matrek Gauss Backward Dan Forward

1/12

SOAL NO 4

X1 X2 X3 b

R(1) 4 -1 0 21

R(2) -1 4 -1 -45

R(3) 0 -1 4 33

Diubah menjadi:

X1 X2 X3 b

R(1) 0 -1 4 33

R(2) 4 -1 0 21

R(3) -1 4 -1 -45

Eliminasi X3

X1 X2 X3 b

R(1) -4 15 0 -147

R(2) 4 -1 0 21

R(3) -1 4 -1 -45

Eliminasi X2

X1 X2 X3 b

R(1) 56 0 0 168

R(2) 4 -1 0 21

R(3) -1 4 -1 -45

SOLUSI:

X1 3X2 -9

X3 6


2/12

SOAL NO 5

X1 X2 X3 b

R(1) 10 1 1 6 R(1)

R(2) 1 10 1 6 R(2)

R(3) 1 1 10 6 R(3)

Eliminasi X3

X1 X2 X3 b

R(1) 99 9 0 54 R(1)

R(2) 9 99 0 54 R(2)

R(3) 1 1 10 6 R(3)

Eliminasi X2

X1 X2 X3 b

R(1) 981818182 0 0 490909091 R(1)

R(2) 9 99 0 54 R(2)

R(3) 1 1 10 6 R(3)

SOLUSI: SOL

X1 05 X1

X2 05 X2

X3 05 X3


3/12

SOAL NO 6

X1 X2 X3 b X1

0 1 7 255 R(1) 5

5 1 0 0 R(2) -2

1 6 1 -105 R(3) 0

Eliminasi X3 Diubah menja

X1 X2 X3 b X1

-7 -41 0 99 R(1) 0

5 1 0 0 R(2) 5

1 6 1 -105 R(3) -2

Eliminasi X2 Eliminasi X3

X1 X2 X3 b X1

198 0 0 99 R(1) -2

5 1 0 0 R(2) 5

1 6 1 -105 R(3) -2

USI: Eliminasi X2

05 X1

-25 R(1) 45890411

4 R(2) 5

R(3) -2

SOLUSI:

X1 2X2 -4

X3 8


4/12

SOAL NO 7 SOAL NO 8

X2 X3 b X1 X2

-2 0 18 R(1) 3 2

10 -2 -60 R(2) 1 3

-2 15 128 R(3) 2 1

i: Eliminasi X3

X2 X3 b X1 X2

-2 15 128 R(1) 7 5

-2 0 18 R(2) -05 35

10 -2 -60 R(3) 2 1

Eliminasi X2

X2 X3 b X1 X2

973333333 0 -429333333 R(1) 771428571 0

-2 0 18 R(2) -05 35

10 -2 -60 R(3) 2 1

SOLUSI:

X2 X3 b X1 2

0 0 917808219 X2 0

-2 0 18 X3 1

10 -2 -60


5/12

SOAL NO 9

X3 b X1 X2 X3

1 7 R(1) 5 1 2

2 4 R(2) 1 4 -2

3 7 R(3) 2 3 8

Eliminasi X3

X3 b X1 X2 X3

0 14 R(1) 18 1 0

0 -1 R(2) 6 19 0

3 7 R(3) 2 3 8

Eliminasi X2

X3 b X1 X2 X3

0 154285714 R(1) 336 0 0

0 -1 R(2) 6 19 0

3 7 R(3) 2 3 8

SOLUSI:

X1 2

X2 1

X3 4


6/12

SOAL NO 10

b X1 X2 X3 b

19 R(1) 4 0 5 125

-2 R(2) 1 6 2 185

39 R(3) 8 2 1 -115

Eliminasi X3

b X1 X2 X3 b

37 R(1) -36 -10 0 70

31 R(2) -15 2 0 415

39 R(3) 8 2 1 -115

Eliminasi X2

b X1 X2 X3 b

672 R(1) -111 0 0 2775

31 R(2) -15 2 0 415

39 R(3) 8 2 1 -115

SOLUSI:

X1 -25

X2 2

X3 45


7/12

SOAL NO 4

X1 X2 X3 b

R(1) 4 -1 0 21 R(1)

R(2) -1 4 -1 -45 R(2)

R(3) 0 -1 4 33 R(3)

Diubah menjadi:

X1 X2 X3 b

R(1) -1 4 -1 -45 R(1)

R(2) 0 -1 4 33 R(2)

R(3) 4 -1 0 21 R(3)

Eliminasi X1

X1 X2 X3 b

R(1) -1 4 -1 -45 R(1)

R(2) 0 -1 4 33 R(2)

R(3) 0 15 -4 -159 R(3)

Eliminasi X2 SOL

X1 X2 X3 b X3

R(1) -1 4 -1 -45 X2

R(2) 0 -1 4 33 X1

R(3) 0 0 37333333333 224

SOLUSI:

X3 6X2 -9

X1 3


8/12

SOAL NO 5

X1 X2 X3 b X1

10 1 1 6 R(1) 0

1 10 1 6 R(2) 5

1 1 10 6 R(3) 1

Eliminasi X1 Diubah menja

X1 X2 X3 b X1

10 1 1 6 R(1) 1

0 99 9 54 R(2) 0

0 9 99 54 R(3) 5

Eliminasi X2 Eliminasi X1

X1 X2 X3 b X1

10 1 1 6 R(1) 1

0 99 9 54 R(2) 0

0 0 1080 540 R(3) 0

USI: Eliminasi X2

05 X1

05 R(1) 1

05 R(2) 0

R(3) 0

SOLUSI:

X3 4X2 -25

X1 05


9/12

SOAL NO 6 SOAL NO 7

X2 X3 b X1 X2

1 7 255 R(1) 5 -2

1 0 0 R(2) -2 10

6 1 -105 R(3) 0 -2

i: Diubah menjadi:

X2 X3 b X1 X2

6 1 -105 R(1) -2 10

1 7 255 R(2) 0 -2

1 0 0 R(3) 5 -2

Eliminasi X1

X2 X3 b X1 X2

6 1 -105 R(1) -2 10

1 7 255 R(2) 0 -2

-29 -5 525 R(3) 0 23

Eliminasi X2

X2 X3 b X1 X2

6 1 -105 R(1) -2 10

1 7 255 R(2) 0 -2

0 682758621 273103448 R(3) 0 0

SOLUSI:

X3 8X2 -4

X1 2


10/12


11/12

SOAL NO 9

b X1 X2 X3 b

7 R(1) 5 1 2 19

4 R(2) 1 4 -2 -2

7 R(3) 2 3 8 39

Eliminasi X1

b X1 X2 X3 b

7 R(1) 5 1 2 19

166666667 R(2) 0 19 -12 -29

233333333 R(3) 0 26 72 314

Eliminasi X2

b X1 X2 X3 b

7 R(1) 5 1 2 19

166666667 R(2) 0 19 -12 -29

257142857 R(3) 0 0 884210526 353684211

SOLUSI:

X3 4

X2 1

X1 2


12/12

SOAL NO 10

X1 X2 X3 b

R(1) 4 0 5 125

R(2) 1 6 2 185

R(3) 8 2 1 -115

Eliminasi X1

X1 X2 X3 b

R(1) 4 0 5 125

R(2) 0 6 075 15375

R(3) 0 2 -9 -365

Eliminasi X2

X1 X2 X3 b

R(1) 4 0 5 125

R(2) 0 6 075 15375

R(3) 0 0 -925 -41625

SOLUSI:

X3 45

X2 2

X1 -25

tugas matrek gauss backward dan forward

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