Question 1043156
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(1) Write the following sets of linear equation in augumented matrix form and solve for x1, x2, and x3 using Gauss Jordan Elimination method: 
(a) 2X1 + X2 - X3 = 8
-3X1 - X2 + 2X3= -11
-2X1 + X2 + 2X3= -3 
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Your matrix

&#8470;	X1	X2	X3	b
1	2	1	-1	8
2	-3	-1	2	-11
3	-2	1	2	3


Make the pivot in the 1st column by dividing the 1st row by 2

&#8470;	X1	X2	X3	b
1	1	1/2	-1/2	4
2	-3	-1	2	-11
3	-2	1	2	3


Eliminate the 1st column

&#8470;	X1	X2	X3	b
1	1	1/2	-1/2	4
2	0	1/2	1/2	1
3	0	2	1	11


Make the pivot in the 2nd column by dividing the 2nd row by 1/2

&#8470;	X1	X2	X3	b
1	1	1/2	-1/2	4
2	0	1	1	2
3	0	2	1	11


Eliminate the 2nd column

&#8470;	X1	X2	X3	b
1	1	0	-1	3
2	0	1	1	2
3	0	0	-1	7


Find the pivot in the 3rd column in the 3rd row (inversing the sign in the whole row)

&#8470;	X1	X2	X3	b
1	1	0	-1	3
2	0	1	1	2
3	0	0	1	-7


Eliminate the 3rd column

&#8470;	X1	X2	X3	b
1	1	0	0	-4
2	0	1	0	9
3	0	0	1	-7


Solution set:

x1 = -4
x2 = 9
x3 = -7
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