# HW #4, due 3:50pm Friday, March 9

(postponed from March 2 because of school closure)

## 2.2

2.2.X (Inverse of product.) (Brought forward from HW#3.) 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.

# HW #5, due 3:50pm Friday, March 9

## 2.8 Subspaces

2.8.2 (Draw two vectors in H and their sum not in H.)

2.8.6 (Is vector in subspace generated by 3 vectors in R4?)

2.8.12 (Where Nul A and Col A "live".)

2.8.22 (True or False statements about column spaces and null spaces.)

2.8.28 (Example of vector not in Col A.)

2.8.29 (Example of vector in Nul A.)

## 2.9 Dimension and rank

2.9.10 (Bases for Col A and Nul A.)

2.9.18 (True or False statements.)