Question

How do you solve this system of equations: `-x + y - z = 2, 2x - 2y - z = - 1 , and 3x + 2y + z = 6`?

Answer 1

The solution is `((x),(y),(z))=((1),(2),(-1))`

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

The augmented matrix is

`A=((-1,1,-1,|,2),(2,-2,-1,|,-1),(3,2,1,|,6))`

Perform the row operations

`R1larrR1xx(-1)`

`A=((1,-1,1,|,-2),(2,-2,-1,|,-1),(3,2,1,|,6))`

`R2larr(R2-2R1)`, and `R3larr(R3-3R1)`

`A=((1,-1,1,|,-2),(0,0,-3,|,3),(0,5,-2,|,12))`

`R2harrR3`

`A=((1,-1,1,|,-2),(0,5,-2,|,12),(0,0,-3,|,3))`

`R3larr(R3/-3)`

`A=((1,-1,1,|,-2),(0,5,-2,|,12),(0,0,1,|,-1))`

`R2larr(R2+2R3)`

`A=((1,-1,1,|,-2),(0,5,0,|,10),(0,0,1,|,-1))`

`R2larr(R2/2)`

`A=((1,-1,1,|,-2),(0,1,0,|,2),(0,0,1,|,-1))`

`R1larr(R1+R2)`

`A=((1,0,1,|,0),(0,1,0,|,2),(0,0,1,|,-1))`

`R1larr(R1-R3)`

`A=((1,0,0,|,1),(0,1,0,|,2),(0,0,1,|,-1))`