Question

How do you solve using gaussian elimination or gauss-jordan elimination, `x+2y+2z=9`, `x+y+z=9`, `3x-y+3z=10`?

Answer 1

`x=9`, `y=17/4` and `z=-17/4`

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

`A=((1,2,2,|,9),(1,1,1,|,9),(3,-1,3,|,10))`

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

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

`A=((1,2,2,|,9),(0,-1,-1,|,0),(0,-7,-3,|,-17))`

`R1larrR1+2R2`; `R3larrR3-7R2`

`A=((1,0,0,|,9),(0,-1,-1,|,0),(0,0,4,|,-17))`

`R2larrR2+1/4R3`

`A=((1,0,0,|,9),(0,-1,0,|,-17/4),(0,0,4,|,-17))`

`R2larr(R2)/(-1)`; `R3larr(R3)/4`

`A=((1,0,0,|,9),(0,1,0,|,17/4),(0,0,1,|,-17/4))`

Thus `x=9`, `y=17/4` and `z=-17/4`