The MATLAB command rand(n) builds an matrix containing pseudo random values in the range drawn from the standard uniform distribution. This means that it is equally probable you will obtain a number...

The MATLAB command rand(n) builds an

matrix containing pseudo random values in the range

drawn from the standard uniform distribution. This means that it is equally probable you will obtain a number from any collection of subintervals of
of the same length; for instance, the chance of obtaining a number from the interval

has the same probability as obtaining a number from the interval

Find the determinant of random matrices of order

and
Does a pattern develop? If you got Inf as output, what does it mean

This interesting problem was described on a MathWorks Web page. The famous Fibonacci numbers are generated from the sequence

Most students have had some exposure to complex numbers. If not, consult Appendix

In the complex number system, the number

so

<sup>2

3

4</sup>

and so forth. MATLAB deals naturally with complex numbers. Create a tridiagonal matrix, with ones on the main diagonal, and

on the first sub and super diagonals with the anonymous function

The command spy(A) produces a placing “*” in locations that are nonzero and leaving the remainder of the figure blank. Verify that the matrix has a tridiagonal pattern by executing the following commands.

Compute the determinants of the sequence of matrices

by executing the loop

Comment on the results.