Question: Read the documentation for your matrix program, and write the commands that will produce the following matrices (without keying in each entry of the matrix).
a. A 4 X 5 matrix of zeros
b. A 5 X 3 matrix of ones
c. The 5 X 5 identity matrix
d. A 4 X 4 diagonal matrix, with diagonal entries 3, 4, 2, 5
A useful way to test new ideas in matrix algebra, or to make conjectures, is to make calculations with matrices selected at random. Checking a property for a few matrices does not prove that the property holds in general, but it makes the property more believable. Also, if the property is actually false, making a few calculations may help to discover this.