 
Summary: 18.024ESG Problem Set 3
Pramod N. Achar
Spring 2000
Tuesday
1. Exercises 12 and 15 in Section 16.20 of Apostol, Volume I.
2. Consider the 2 × 3 matrix
P =
1 2 3
4 5 6
.
(a) Show that P has no left inverse, and find at least two right inverses
for it. (Remember that any left or right inverse should be a 3 × 2
matrix.)
(b) (Optional) Find the set of all right inverses of P. If you think of 3×2
matrices as a way of writing down vectors in R6
, then the set of all
right inverses of P is some plane in R6
. Give a parametric equation
for this plane. What is its dimension?
Thursday
