# Solving system of equations Mathematica

• Mathematica
I am solving the following system of equations (in matrix form):

##\begin{pmatrix} 1 & -2 & -1 & 1 \\ 2 & -3 & 1 & 6 \\ 3 & -5 & 0 & 7 \\ 1 & 0 & 5 & 9 \end{pmatrix}##

I want to solve it using Mathematica, but when I use the command LinearSolve[], I only get back ##\begin{pmatrix} 9 \\ 4 \\ 0 \end{pmatrix}##, which is a particular solution. However, I am looking for how to get an output of something like ##\begin{pmatrix} 9 \\ 4 \\ 0 \end{pmatrix} + t_1\begin{pmatrix} -5 \\ -3 \\ 1 \end{pmatrix}##, where the linear combinations of the basis for the kernel is included. Is there a single command that does this? Or would I have to separately the NullSpace[] command?

Buzz Bloom
Gold Member
Hi Mr Davis:

I know next to nothing about Mathematica, but I would expect it to have a function you could invoke that would invert a matrix for you. Did you look for one to do that?