how do you solve this using a gausian reduction using the three equations? 4x+z=3,2x-y=2,and 3y+2z=0

Question

I think gaussian reduction is similar to back substitution, but with all the equation shaving different variables... just not sure how to do it.

Answer 1

Gven equations are 4x+z = 3 ---> (1)

2x-y = 2 -----> (2)

3y+2z = 0 -----> (3)

Here to solve the equations use gussian reduction method

Convert three equations in to matrices form.

By the gussian reduction method the augment matrix is

Observe the above  matrix the elements of forth column would be the solutions of given equations.

x = 0, y = -2, z = 3