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Question 815171: 1. Solve the following equations using Gauss Elimination method.
2x+4y+z=3, 3x+2y-2z=-2 , x-y+z=6
2. Solve the system of equations by Jacobi’s iterative method (calculate three iterations only.)
20x+y-2z=17, 3x+20y-z=-18, 2x-3y+20z=25
3. Find the values of x,y and z using Gauss Seidal method.
83x-11y-4z =95 , 7x+52y+13z =104, 3x+8y+29z =71
4. Solve the system of equations by Gauss Jordan method:
3x+2y+7z=4, 2x+3y+z=5, 3x+4y+z=7
5. Solve the system of equations by matrix inversion method:
5x+3y+7z=4, 3x+26y+2z=9, 7x+2y+11z =5
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! You should not include so many problems (especially such labor-intensive ones) in a single post. I will do the first one for you. Re-post the others separately if you want more help.
Note: Algebra.com's formula drawing software does not do matrices very well. So I am going to just show the rectangular array of numbers without the brackets which usually indicate a matrix.
2x+4y+z=3
3x+2y-2z=-2
x-y+z=6
The augmented matrix:
2 4 1 3
3 2 -2 -2
1 -1 1 6
Replace row 1 with 1/2 times row 1:
1 2 1/2 3/2
3 2 -2 -2
1 -1 1 6
Add -3 times row 1 to row 2:
1 2 1/2 3/2
0 -4 -7/2 -13/2
1 -1 1 6
Add -1 times row 1 to row 3:
1 2 1/2 3/2
0 -4 -7/2 -13/2
0 -3 1/2 9/2
Replace row 2 with -1/4 times row 2:
1 2 1/2 3/2
0 1 7/8 13/8
0 -3 1/2 9/2
Add -2 times row 2 to row 1:
1 0 -5/4 -7/4
0 1 7/8 13/8
0 -3 1/2 9/2
Add 3 times row 2 to row 3:
1 0 -5/4 -7/4
0 1 7/8 13/8
0 0 25/8 75/8
Replace row 3 with 8/25 times row 3:
1 0 -5/4 -7/4
0 1 7/8 13/8
0 0 1 3
Add 5/4 times row 3 to row 1
1 0 0 2
0 1 7/8 13/8
0 0 1 3
Add -7/8 times row 3 to row 2:
1 0 0 2
0 1 0 -1
0 0 1 3
This translates into:
x = 2
y = -1
z = 3
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