# What can I use to solve a general matrix?

1. Oct 17, 2011

### VortexLattice

Hi guys!

I need to solve a matrix. I have 3 equations, 3 unknowns, straightforward stuff. And I know it's invertible (doing transformations for hamiltonian dynamics, so I know they made it invertible). I know my calculator and a ton of websites can easily solve any matrix with real coefficients, but here they are general variables.

Does anyone know a good website (or how to do it on the TI-83, or TI-89) that will do this?

For example, solving something like:

a*x + b*y = 3
ba*x + 4b*y = 5, finding x and y as functions of a and b.

Any good way?

Thanks!

2. Oct 17, 2011

### phyzguy

This is of the form M.X = S, so the solution is just $$M^{-1}.S$$ .

Wolfram alpha (http://www.wolframalpha.com) will solve this easily. The syntax is :

Inverse[{{a, b}, {a b, 4 b}}].{3,5}//Simplify

Try it!

3. Oct 18, 2011

### hotvette

You can solve the example by substitution. Solve the 1st equation for either x or y and substitute the result into the 2nd equation to solve for the other unknown. You'll end up with algebraic expressions for x and y in terms of a and b.

4. Oct 18, 2011

### jasonRF

Phyzguy recommended wolfram alpha, which is a great option. Maxima is another option, possibly more clunky but I use it the most for computer algebra and arbitrary precision arithmetic:

http://maxima.sourceforge.net/

enjoy,

jason