Question 1182942
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4x1 - 3x2 + x3 = -8
-2x1 + x2 - 3x3 = -4
x1 - x2 + 2x3 = 3
 
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)

4	-3	1	-8
-2	1	-3	-4
1	-1	2	3
 
R1 / 4 → R1 (divide the 1 row by 4)

1	-0.75	0.25	-2
-2	1	-3	-4
1	-1	2	3
 
R2 + 2 R1 → R2 (multiply 1 row by 2 and add it to 2 row); R3 - 1 R1 → R3 (multiply 1 row by 1 and subtract it from 3 row)

1	-0.75	0.25	-2
0	-0.5	-2.5	-8
0	-0.25	1.75	5
 
R2 / -0.5 → R2 (divide the 2 row by -0.5)

1	-0.75	0.25	-2
0	1	5	16
0	-0.25	1.75	5
 
R1 + 0.75 R2 → R1 (multiply 2 row by 0.75 and add it to 1 row); R3 + 0.25 R2 → R3 (multiply 2 row by 0.25 and add it to 3 row)

1	0	4	10
0	1	5	16
0	0	3	9
 
R3 / 3 → R3 (divide the 3 row by 3)

1	0	4	10
0	1	5	16
0	0	1	3
 
R1 - 4 R3 → R1 (multiply 3 row by 4 and subtract it from 1 row); R2 - 5 R3 → R2 (multiply 3 row by 5 and subtract it from 2 row)

1	0	0	-2
0	1	0	1
0	0	1	3
 
x1 = -2
x2 = 1
x3 = 3
 
Make a check:

4·(-2) - 3·1 + 3 = -8 - 3 + 3 = -8
-2·(-2) + 1 - 3·3 = 4 + 1 - 9 = -4
(-2) - 1 + 2·3 = -2 - 1 + 6 = 3

Check completed successfully.


<U>ANSWER</U>

x1 = -2
x2 = 1
x3 = 3
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