**1.9.38** (Is transformation *1-to-1*?

**1.9.40** (Is transformation *onto*.)

**1.10.12** (Rental car migration.)

Note: this kind of a model really only applies well to systems where the numbers of items are *large*,
so that effects of randomness are not important. A bit dubious with the numbers in this exercise.

**2.1.12** (Demonstration that AB=0 does *not* imply A=0 or B=0.)

**2.1.22** (L.D. of columns of B implies L.D. of columns of AB.)

Hints: The approach here is to "unpack" the two statements "columns of B are L.D." and "columns of AB are L.D." (I mean translate each of them to a sentence that begins "There exists ..") and then show the former implies the latter. To do this, you will need to invoke the associativity of matrix multiplication.

**2.2.X** (Inverse of product.) This was accidentally not published until quite late, so will be ncluded in Homework #4 instead.
Your random matrix should of course be different from mine, and that of all other students.

a. Construct 2 largish (at least 5x5) random square matrices, A and B, with integer values. Form the product AB.

b. Use the algorithm I showed you in class on Feb 20 to find the inverses of A, B and AB.

c.
Show that, at least in this case, the inverse of AB is the product of the inverses
of A and B *in reverse order*.