Solve the system of linear equations using the gauss-jordan elimination method.
(x, y,z)=
2x + 2y − 3z = 16
2x − 3y + 2z = −4
4x − y + 3z =
−4

(x,y,z)=(2,0,-4)

Step-by-step explanation:

First we create the extended matrix from the equations

Using the elementary operations

Substract to the 2nd line the first one, and the 3rd one twice the first:

Divide the first line by 2, the 2nd one by -5 and substract to the 3rd the 2nd:

Divide the 3rd by 4:

Add the 3rd to the 2nd:

Substract the 2nd to the 1st

Add the 3rd multiplied by 3/2:

The answer is determined:

x=2

y=0

z=-4

You can check they are correct, by entering in the original formulas.

Answers4.) -1/205.) -1/406.) -55/127.) -3/4