Answer:
Option B is correct!
Step-by-step explanation:
solving using Gauss-Jordan elimination
x y z b
1 1 1 1 2
2 2 -3 1 -11
3 -1 2 -1 8
Finding the pivot in the 1st column in the 1st row
x y z b
1 1 1 1 2
2 2 -3 1 -11
3 -1 2 -1 8
Multiplying the 1st row by 2
x y z b
1 2 2 2 4
2 2 -3 1 -11
3 -1 2 -1 8
Subtract the 1st row from the 2nd row and restore it
x y z b
1 1 1 1 2
2 0 -5 -1 -15
3 -1 2 -1 8
Multiplying the 1st row by -1
x y z b
1 -1 -1 -1 -2
2 0 -5 -1 -15
3 -1 2 -1 8
Subtract the 1st row from the 3rd row and restore it
x y z b
1 1 1 1 2
2 0 -5 -1 -15
3 0 3 0 10
Make the pivot in the 2nd column by dividing the 2nd row by -5
x y z b
1 1 1 1 2
2 0 1 1/5 3
3 0 3 0 10
Subtracting the 2nd row from the 1st row
x y z b
1 1 0 4/5 -1
2 0 1 1/5 3
3 0 3 0 10
Multiplying the 2nd row by 3
x y z b
1 1 0 4/5 -1
2 0 3 3/5 9
3 0 3 0 10
Subtracting the 2nd row from the 3rd row
x y z b
1 1 0 4/5 -1
2 0 1 1/5 3
3 0 0 -3/5 1
Making the pivot in the 3rd column by dividing the 3rd row by -3/5
x y z b
1 1 0 4/5 -1
2 0 1 1/5 3
3 0 0 1 -5/3
Multiplying the 3rd row by 4/5
x y z b
1 1 0 4/5 -1
2 0 1 1/5 3
3 0 0 4/5 -4/3
Subtracting the 3rd row from the 1st row and restore it
x y z b
1 1 0 0 1/3
2 0 1 1/5 3
3 0 0 1 -5/3
Multiply the 3rd row by 1/5
x y z b
1 1 0 0 1/3
2 0 1 1/5 3
3 0 0 1/5 -1/3
Subtract the 3rd row from the 2nd row and restore it
x y z b
1 1 0 0 1/3
2 0 1 0 10/3
3 0 0 1 -5/3
Here
x = 1/3
y = 10/3
z=-5/3
