# How Do I Solve a System with Inverses Using WolframAlpha?

In the handout

I showed you how to find the inverse of a coefficient matrix. I also showed how to used it to solve the system

5+ 7+ 12= 134,000
2+ 3+ 5= 56,000
= 14,000

In this post, I want to show you how to solve this system using WolframAlpha.

Start by writing the coefficient and constant matrices for this system,

$latex \displaystyle A=\left[ \begin{matrix} 5 & 7 & 12 \\ 2 & 3 & 5 \\ 1 & 1 & 1 \\ \end{matrix} \right]$

and

$latex \displaystyle B=\left[ \begin{matrix} 134000 \\ 56000 \\ 14000 \\ \end{matrix} \right]$

We can solve the system by computing $latex \displaystyle X={{A}^{-1}}B$.

Using WolframAlpha, we can find the inverse of A: Notice that each row of the matrix must be entered in brackets. Now multiply the inverse by the constant matrix to get the solution of the system. This is the same as the solution from the calculator,

$latex \displaystyle X=\left[ \begin{matrix} 2000 \\ 4000 \\\ 8000 \ \end{matrix} \right]$