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Algebra - Gauss-Jordan Elimination

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4x(1) + 5x(2) + 2x(3) = 11
2x(2) + 3x(3) - 4x(4) = -2
2x(1) + x(2) + 3x(4) = 12
x(1) + x(3) + x(4) = 9

Using a Gauss-Jordan Elimination process, x (1) =

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4x(1) + 5x(2) + 2x(3) = 11
2x(2) + 3x(3) - 4x(4) = -2
2x(1) + x(2) + 3x(4) = 12
x(1) + x(3) + x(4) = 9

Using a Gauss-Jordan Elimination process, x (1) =

Row
Operation
1: 4 5 2 0 11
0 2 3 -4 -2
2 1 0 3 12
1 0 1 1 9

multiply the 1st row by 1/4 1 5
________________________________________ 4 1
________________________________________ 2 0 11
________________________________________ 4
0 2 3 -4 -2
2 1 0 3 12
1 0 1 1 9

Row
Operation
2: 1 5
________________________________________ 4 1
________________________________________ 2 0 11
________________________________________ 4
0 2 3 -4 -2
2 1 0 3 12
1 0 1 1 9

add -2 times the 1st row to the 3rd row 1 5
________________________________________ 4 1
________________________________________ 2 0 11
________________________________________ 4
0 2 3 -4 -2
0 -3
________________________________________ 2 -1 3 13
________________________________________ 2
1 0 1 1 9

Row
Operation
3: 1 5
________________________________________ 4 1
________________________________________ 2 0 11
________________________________________ 4
0 2 3 -4 -2
0 -3
________________________________________ 2 -1 3 13
________________________________________ 2
1 0 1 1 9

add -1 times the 1st row to the 4th row 1 5
________________________________________ 4 1
________________________________________ 2 0 11
________________________________________ 4
0 2 3 -4 -2
0 -3
________________________________________ 2 -1 3 13
________________________________________ 2
0 -5
________________________________________ 4 1
________________________________________ 2 1 25
________________________________________ 4

Row
Operation
4: 1 5
________________________________________ 4 1
________________________________________ 2 0 11
________________________________________ 4
0 2 3 -4 -2
0 -3
________________________________________ 2 -1 3 13
________________________________________ 2
0 -5 ...

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