Question

Solve using Gaussian Elimination with back subsitution:

3x(1) - 2x(2) + x(3) =3

2x(1) + 4x(2) - 2x(3) = 2

4x(1) - 2x(2) - 3x(2) = -12

Answer 1

system is

augmented matrix is

3	-2	1	3
2	4	-2	2
4	-2	-3	-12

convert into Row Eschelon Form...

Divide row1 by 3

1	-2/3	1/3	1
2	4	-2	2
4	-2	-3	-12

Add (-2 * row1) to row2

1	-2/3	1/3	1
0	16/3	-8/3	0
4	-2	-3	-12

Add (-4 * row1) to row3

1	-2/3	1/3	1
0	16/3	-8/3	0
0	2/3	-13/3	-16

Divide row2 by 16/3

1	-2/3	1/3	1
0	1	-1/2	0
0	2/3	-13/3	-16

Add (-2/3 * row2) to row3

1	-2/3	1/3	1
0	1	-1/2	0
0	0	-4	-16

Divide row3 by -4

1	-2/3	1/3	1
0	1	-1/2	0
0	0	1	4

from the last row

from the second row

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from the first row

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solution is