Can most programs (except the IO part) be re-written as a sequence of matrix operations?
If you regard the output of a program as a function of its input then matrices can be used to represent some programs, namely those where the output is a linear function of the input. So a program that takes two arguments $a$ and $b$ and returns $a+b$ and $a-b$ could be represented by the matrix

$\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; -1 \end{pmatrix}$

But most programs are not linear functions. For example, if the program instead returns $a^2+b^2$ and $a^2-b^2$ how will you represent that as a matrix ?