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Doug poses a good question, which one of the software packages is better.

We you should probably also throw at least Maple into the mix. You can accomplish a lot of the same with any of them. I believe Matlab was originally designed for numerical computations involving large matrices. Prior to this one had to write or use a commercial Fortran subroutine to solve a linear system by Gaussian elimination. In Matlab this and other standard computations are built-in commands.

On the other hand Mathematica, like Maple, was designed with symbolic calculations foremost in mind. While it is certainly true that numerical computations can be done with Mathematica, this is typically not the driving force in choosing to use this program.