Question

How do you solve the system `x+3y-2z=8`, `3x+2y-3z=15`, and `4x+2y+3z=-1`?

Answer 1

`x=134/47`, `y=24/47` and `z=-85/47`

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

`A=((1,3,-2,|,8),(3,2,-3,|,15),(4,2,3,|,-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

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

`A=((1,3,-2,|,8),(0,-7,3,|,-9),(0,-10,11,|,-25))`

`R2larrR2-R3`

`A=((1,3,-2,|,8),(0,3,-8,|,16),(0,-10,11,|,-25))`

`R1larrR1-R2`

`A=((1,0,6,|,-8),(0,3,-8,|,16),(0,-10,11,|,-25))`

`R2larr(R2)/3`

`A=((1,0,6,|,-8),(0,1,-8/3,|,16/3),(0,-10,11,|,-25))`

`R3larrR3+10R2`

`A=((1,0,6,|,-8),(0,1,-8/3,|,16/3),(0,0,-47/3,|,85/3))`

`R3larrR3*(-3)/47`

`A=((1,0,6,|,-8),(0,1,-8/3,|,16/3),(0,0,1,|,-85/47))`

`R1larrR1-6R3` ; `R2larrR2+8/3R3`

`A=((1,0,0,|,134/47),(0,1,0,|,24/47),(0,0,1,|,-85/47))`

Thus `x=134/47`, `y=24/47` and `z=-85/47`