Question

How do you solve the system `9x + 9y + z = -112`, `8x + 5y - 9z = -137`, `7x + 4y + 3z = -64`?

Answer 1

`x=-9`, `y=-4` and `z=5`

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

`A=((9,9,1,|,-112),(8,5,-9,|,-137),(7,4,3,|,-64))`

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

`R2larrR1-R2`; `R3larrR3-R2`

`A=((1,4,10,|,25),(8,5,-9,|,-137),(-1,-1,12,|,73))`

`R2larrR2-8R1`; `R3larrR3+R1`

`A=((1,4,10,|,25),(0,-27,-89,|,-337),(0,3,22,|,98))`

`R2larrR2+9R3`

`A=((1,4,10,|,25),(0,0,109,|,545),(0,3,22,|,98))`

`R2larr(R2)/109`

`A=((1,4,10,|,25),(0,0,1,|,5),(0,3,22,|,98))`

`R1larrR1-10R2`; `R3larrR3-22R2`

`A=((1,4,0,|,-25),(0,0,1,|,5),(0,3,0,|,-12))`

`R3larr(R3)/3`

`A=((1,4,0,|,-25),(0,0,1,|,5),(0,1,0,|,-4))`

`R1larrR1-4R3`

`A=((1,0,0,|,-9),(0,0,1,|,5),(0,1,0,|,-4))`

Thus `x=-9`, `y=-4` and `z=5`