Question

How to solve the system of equation using matrices? Thanks!

Answer 1

`x=1`, `y=-4` and `z=-2`

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

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

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`; `R3larrR3-4R1`

`A=((1,1,1,|,-5),(0,-2,2,|,4),(0,-3,-3,|,18))`

`R2larr(R2)/(-2)`

`A=((1,1,1,|,-5),(0,1,-1,|,-2),(0,-3,-3,|,18))`

`R3larrR3+3R2`

`A=((1,1,1,|,-5),(0,1,-1,|,-2),(0,0,-6,|,12))`

`R3larr(R2)/(-6)`

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

`R1larrR1-R3; R2larrR2+R3`

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

`R1larrR1-R2`

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

Thus, `x=1`, `y=-4` and `z=-2`