Question

How do you solve using gaussian elimination or gauss-jordan elimination, `2x-3y-2z=10`, `3x-2y+2z=0`, `4z-y+3z=-1`?

Answer 1

`x=2`, `y=0` and `z=-3`

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

`A=((2,-3,-2,|,10),(3,-2,2,|,0),(4,-1,3,|,-1))`

I have written the equations not in the sequence as in the question in order to get `1` as pivot.

Perform the folowing operations on the rows of the matrix

`R1larrR1+R2`

`A=((5,-5,0,|,10),(3,-2,2,|,0),(4,-1,3,|,-1))`

`R1larr(R1)/5`

`A=((1,-1,0,|,2),(3,-2,2,|,0),(4,-1,3,|,-1))`

`R2larrR2-3R1`; `R3larrR3-4R1`

`A=((1,-1,0,|,2),(0,1,2,|,-6),(0,3,3,|,-9))`

`R3larrR3-3R2`

`A=((1,-1,0,|,2),(0,1,2,|,-6),(0,0,-3,|,9))`

`R3larrR3/(-3)`

`A=((1,-1,0,|,2),(0,1,2,|,-6),(0,0,1,|,-3))`

`R2larrR2-2R3`

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

`R1larrR1+R2`

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

Thus `x=2`, `y=0` and `z=-3`