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Solve the following system, using Gaussian elimination with partial pivoting. Round everyfigure, including intermediate calculations, to exactly three significant digits.1 216 3 4731521X3

Question
Solve the following system, using Gaussian elimination with partial pivoting. Round every
figure, including intermediate calculations, to exactly three significant digits.
1 2
1
6 3 4
7
3
1
5
21
X3
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Solve the following system, using Gaussian elimination with partial pivoting. Round every figure, including intermediate calculations, to exactly three significant digits. 1 2 1 6 3 4 7 3 1 5 21 X3

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check_circleAnswer
Step 1

Given,

1 21X1]
ГЗ
6 3 42=
|X3
Г14]
7
[21.
3 1 5x3_
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1 21X1] ГЗ 6 3 42= |X3 Г14] 7 [21. 3 1 5x3_

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Step 2

Solving by Gaussian elimination with partial pivoting method

21TX1
6 3 4X2
3 1 5||x3
3
1
[14]
7
21.
Here, pivot element is 6 in first column. So, interchanging the 1st and 2nd row.
Г6
R2R1
3
3 4111
2|X2
5 LX3
7
1
14
3
[21.
1
0.5
Г1
0.6671
|X2
|X3.
[1.167
3
1
2
14
3
5
1
21
0.5
0.6671[X11
[1.167
1
0 0.5
R23R1-R2
0
-10.5
Хз.
5
21
3
1
0.6671 [X1
2
Хз.
0.5
1
0 0.5
Lo 0.5
[1.167
R3 3R1-R3
0
-10.5
[-17.5]
-3
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21TX1 6 3 4X2 3 1 5||x3 3 1 [14] 7 21. Here, pivot element is 6 in first column. So, interchanging the 1st and 2nd row. Г6 R2R1 3 3 4111 2|X2 5 LX3 7 1 14 3 [21. 1 0.5 Г1 0.6671 |X2 |X3. [1.167 3 1 2 14 3 5 1 21 0.5 0.6671[X11 [1.167 1 0 0.5 R23R1-R2 0 -10.5 Хз. 5 21 3 1 0.6671 [X1 2 Хз. 0.5 1 0 0.5 Lo 0.5 [1.167 R3 3R1-R3 0 -10.5 [-17.5] -3

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Step 3

Since, all the elements are 2nd column are same so piv...

1.167
R3-R2-R3 0.5 0.6671
0 0.5
Lo
X2
X3.
-10.5
0
0
3
7
Thus, 3x3 7
x3 = 2.333
And 0.5x2 -10.5
X2=-21
x1 0.5x2 0.667x3 = 1.167
10.5)+0.667(2.333) = 1.167
x1
x1 = 10.110889
x110.111
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1.167 R3-R2-R3 0.5 0.6671 0 0.5 Lo X2 X3. -10.5 0 0 3 7 Thus, 3x3 7 x3 = 2.333 And 0.5x2 -10.5 X2=-21 x1 0.5x2 0.667x3 = 1.167 10.5)+0.667(2.333) = 1.167 x1 x1 = 10.110889 x110.111

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