MATLAB Tutor

Part 9: Symbolic Matrices

MATLAB's Symbolic Math Toolbox allows you to use symbols when doing matrix algebra.

1. Whenever you want to define a matrix that includes symbols, you must first declare those variables symbolic by using the "syms" command. Enter
   
        syms t   % t is a symbolic variable
        A = [cos(t) sin(t); -sin(t) cos(t)]
        det(A)
        best = simple(ans)
2. Compare the result of step 1 to the one you get when you enter the following statements:
   
        t = 5   % t has a numeric value
        format short    % show decimal format
        A = [cos(t) sin(t); -sin(t) cos(t)]
        det(A)
3. It is just as easy to declare two or more variables symbolic as one. Enter
   
        syms a b c d   % Create symbolic variables
        M = [a b; c d]   % Create a symbolic matrix
        det (M)   % Find the determinant of M
   
   Did you get the answer you expected?
4. Enter the following set of commands. Be sure you understand what happens after each one is performed.
   
        syms  lambda
        A = [1 2; 3 8]
        I = eye(2)
        M = A - lambda*I
        cpoly = det(M)
        solve(cpoly)   % roots of quadratic
        double(ans)

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