Linear Algebra with Applications, 10th Edition

Symbolic Toolbox

In addition to doing numeric computations, it is possible to do symbolic calculations with MATLAB’s symbolic toolbox. The symbolic toolbox allows us to manipulate symbolic expressions. It can be used to solve equations, differentiate and integrate functions, and perform symbolic matrix operations.

MATLAB’s sym command can be used to turn any MATLAB data structure into a symbolic object. For example, the command sym(‘t’) will turn the string ‘t’ into a symbolic variable t, and the command sym(hilb(3)) will produce the symbolic version of the $3\times 3$ Hilbert matrix written in the form

$$\begin{array}{c}\left[\begin{array}{ccc}1,& \frac{1}{2},& \frac{1}{3}\end{array}\right]\\ \left[\begin{array}{ccc}\frac{1}{2},& \frac{1}{3},& \frac{1}{4}\end{array}\right]\\ \left[\begin{array}{ccc}\frac{1}{3},& \frac{1}{4},& \frac{1}{5}\end{array}\right]\end{array}$$

We can create a number of symbolic variables at once with the syms command. For example, the command

$$\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\begin{array}{c}\mathsf{\text{syms}}\end{array}& \mathsf{a}\end{array}& \mathsf{b}\end{array}& c\end{array}$$

creates ...