Overview
only problem 4 and 5 are required to do
4. Consider the following three matrices:
A =
·
2 3 ?1
?1 0 ?1
?
, B =
£
3 3¤
, C =
?
?
2
2
3
?
? . (4)
For each possible choice of two of these three matrices, discuss whether they can be multiplied
together (order matters). Whenever the multiplication is possible, specify what size the resulting
product matrix should have, then compute it.
For each of the matrices you obtain (after multiplication), determine the dimension of its null
space, column space, and row space.
5. Consider the vectors
?a =
?
?
2
2
3
?
? , ?b =
?
?
1
?1
0
?
? , ?c =
?
?
?3
0
2
?
? (5)
from Question 1. Suppose that T : R
3 ? R
3
is a linear transformation such that
T (?a) = T (?b) =?c and T (?c) =?b . (6)
What can you deduce about the null space and range of T ?