Chapter 3

Question 1

Definition of a linear map

Answer 1

Bl1

Question 2

Lemma 30:

Suppose T: V->W is a linear map, then?

Answer 2

Bl1

Question 3

What is a composition of linear maps?

Answer 3

Bl1

Question 4

When is a linear map isomorphic?

Answer 4

Bl1

Question 5

What is vecV,B(c)

Answer 5

Bl2

Question 6

Let T: V -> W be a linear map of a vector space V to a vector space W. Let B equal b1, b2, b3,…,bm
Let C equal c1,….,cm
What is the matrix of T with repect to bases B and C?

Answer 6

Bl2

Question 7

Let T: V -> W be a linear map of a vector space V to a vector space W. Let B equal b1, b2, b3,…,bm
Let C equal c1,….,cm
Then for all vectors v in V?

Answer 7

Bl3

Question 8

What is Kernal of T?

Answer 8

Bl3

Question 9

What is the Image of T

Answer 9

Bl3

Question 10

Prove that two finite dimensional vector spaces V and W are isomorphic iff they have the same dimension

Answer 10

Bl 5

Question 11

Prove theorem [T(v)]c=[T]c

Answer 11

Bl6

Question 12

What is a composite map?

Prove it

Answer 12

Bl7

Question 13

What is the functionality of the matrix of a linear map?

Answer 13

Bl8

Question 14

What is the rank nullity theorem?

Answer 14

Bl9