Question

Solve: 2x+3y+z=-3
x+4y-3z=-23
3x-y+2z=14

Answer 1

do you know how to use matrix or just algebra...?

Answer 2

Algebra

Answer 3

I looked at this thing and decided to use Mathematica to solve it.
\[\text{Solve}[\{2x+3y+z\text{==}-3, x+4y-3z\text{==}-23 ,3x-y+2z\text{==}14\},\{x,y,z\}] \]={{x -> 1, y -> -3, z -> 4}}

Feeding the solutions for x, y and z back into the equations show that they are the roots.
\[\{2x+3y+z\text{=}-3, x+4y-3z\text{=}-23 ,3x-y+2z\text{=}14\}\text{/.}\{x\to 1,y\to -3,z\to 4\} \]={True, True, True}
True means that the left hand side and the right hand side of each equation is equal.

Answer 4

Mathematica can deal with matix expressions, however, I cannot. In the case of these three equations the setup is much easier to use Solve rather than LinearSolve.

Sorry.