Linear Equations with 5 Unknowns

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Please see the attachment for solution to the system of linear equations in 5 unknowns.

Solve the system:
{x+2y-z+2w+3t=11
{x-y+2z-w+2t=0
{2x+y-z+2w-t=4
{3x+2y-z+w-2t=2
{2x+y-z-2w+t=4 Let x = x1, y = x2, z = x3, w = x4 and t = x5.
Step 1: Transform the augmented matrix to the reduced row echelon form

Row
Operation
1: 1 2 -1 2 3 11
1 -1 2 -1 2 0
2 1 -1 2 -1 4
3 2 -1 1 -2 2
2 1 -1 -2 1 4

add -1 times the 1st row to the 2nd row 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
2 1 -1 2 -1 4
3 2 -1 1 -2 2
2 1 -1 -2 1 4

Row
Operation
2: 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
2 1 -1 2 -1 4
3 2 -1 1 -2 2
2 1 -1 -2 1 4

add -2 times the 1st row to the 3rd row 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
0 -3 1 -2 -7 -18
3 2 -1 1 -2 2
2 1 -1 -2 1 4

Row
Operation
3: 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
0 -3 1 -2 -7 -18
3 2 -1 1 -2 2
2 1 -1 -2 1 4

add -3 times the 1st row to the 4th row 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
0 -3 1 -2 -7 -18
0 -4 2 -5 -11 -31
2 1 -1 -2 1 4

Row
Operation
4: 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
0 -3 1 -2 -7 -18
0 -4 2 -5 -11 -31
2 1 -1 -2 1 4

add -2 times the 1st row to the 5th row 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
0 -3 1 -2 -7 -18
0 -4 2 -5 -11 -31
0 -3 1 -6 -5 -18

Row
Operation
5: 1 2 -1 2 3 11
0 -3 3 -3 -1 -11
0 -3 1 -2 -7 -18
0 -4 2 -5 -11 -31
0 -3 1 -6 -5 -18

multiply the 2nd row by -1/3 1 2 -1 2 3 11
0 1 -1 1 1
________________________________________ 3 11
________________________________________ 3
0 -3 1 -2 -7 -18
0 -4 2 -5 -11 -31
0 -3 1 -6 -5 -18

Row
Operation
6: 1 2 -1 2 3 11
0 1 -1 1 1
________________________________________ 3 11
________________________________________ 3
0 -3 1 -2 -7 -18
0 -4 2 -5 -11 -31
0 -3 1 -6 -5 -18

add 3 times the 2nd row to the 3rd row 1 2 -1 2 3 11
0 1 -1 1 1
________________________________________ 3 11
________________________________________ 3
0 0 -2 1 -6 -7
0 -4 2 -5 -11 -31
0 -3 1 -6 -5 -18

Row
Operation
7: 1 2 -1 2 3 11
0 1 -1 1 1
________________________________________ 3 11
________________________________________ 3
0 0 -2 1 -6 -7
0 -4 2 -5 -11 -31
0 -3 1 -6 -5 -18

add 4 times the 2nd row to the 4th row 1 2 -1 2 3 11
0 1 -1 1 1
________________________________________ 3 11
________________________________________ 3
0 0 -2 1 -6 -7
0 0 -2 -1 -29
________________________________________ 3 -49
________________________________________ 3
0 -3 1 -6 -5 -18

Row
Operation
8: 1 2 -1 2 3 11
0 1 -1 1 1
________________________________________ 3 11
________________________________________ 3
0 0 -2 1 -6 -7
0 0 -2 -1 -29
________________________________________ 3 -49
________________________________________ 3
0 -3 1 -6 -5 -18

add 3 times the 2nd row to ...