Experiment with the random commands to generate 10

Chapter , Problem 1E

(choose chapter or problem)

Problem 1E

Experiment with the random commands to generate 10 different homogeneous (in × n) systems with integer entries, the entries between − 20 and 20. Make sure at least 6 of your systems have n larger than m.

Solve the system by first using the rref command. Then use pencil and paper to find the form of the solutions. What can you conclude if n is larger than m? Compare to Theorem 4. (Note: You might notice that both you and a classmate get the same matrix

when you type r a n d (2 ,3). This is because MATLAB has a default system of selecting the seed for its random number generator. To personalize the rand command type

≫ rand ('seed ', 'your first ame your lastname ')

You only need to type this once before you use the first r a n d command. Do not forget the single quotations. (Of course, in practice you can type anything between the second set of single quotations.)