gistfile1.txt

Solve the following system:
{2x+y-2z = 10
3x+2y+2z = 1
5x+4y+3z = 4
Express the system in matrix form:
(2 | 1 | -2
 3 | 2 | 2
 5 | 4 | 3)(x
y
z) = (10
1
4)
Write the system in augmented matrix form and use Gaussian elimination:
(2 | 1 | -2 | 10
 3 | 2 | 2  | 1
 5 | 4 | 3  | 4)
Swap row 1 with row 3:
(5 | 4 | 3  | 4
 3 | 2 | 2  | 1
 2 | 1 | -2 | 10)
Subtract 3/5 × (row 1) from row 2:
(5 | 4    | 3   | 4
 0 | -2/5 | 1/5 | -7/5
 2 | 1    | -2  | 10)
Multiply row 2 by 5:
(5 | 4  | 3  | 4
 0 | -2 | 1  | -7
 2 | 1  | -2 | 10)
Subtract 2/5 × (row 1) from row 3:
(5 | 4    | 3     | 4
 0 | -2   | 1     | -7
 0 | -3/5 | -16/5 | 42/5)
Multiply row 3 by 5:
(5 | 4  | 3   | 4
 0 | -2 | 1   | -7
 0 | -3 | -16 | 42)
Swap row 2 with row 3:
(5 | 4  | 3   | 4
 0 | -3 | -16 | 42
 0 | -2 | 1   | -7)
Subtract 2/3 × (row 2) from row 3:
(5 | 4  | 3    | 4
 0 | -3 | -16  | 42
 0 | 0  | 35/3 | -35)
Multiply row 3 by 3/35:
(5 | 4  | 3   | 4
 0 | -3 | -16 | 42
 0 | 0  | 1   | -3)
Add 16 × (row 3) to row 2:
(5 | 4 | 3  | 4
 0 | -3 | 0 | -6
 0 | 0 | 1  | -3)
Divide row 2 by -3:
(5 | 4 | 3 | 4
 0 | 1 | 0 | 2
 0 | 0 | 1 | -3)
Subtract 4 × (row 2) from row 1:
(5 | 0 | 3 | -4
 0 | 1 | 0 | 2
 0 | 0 | 1 | -3)
Subtract 3 × (row 3) from row 1:
(5 | 0 | 0 | 5
 0 | 1 | 0 | 2
 0 | 0 | 1 | -3)
Divide row 1 by 5:
(1 | 0 | 0 | 1
 0 | 1 | 0 | 2
 0 | 0 | 1 | -3)
Collect results:
Answer: |  
 | {x = 1
y = 2
z = -3