Unit 3

Question 1

There are L.T between vector spaces of different dimensions?

Answer 1

Yes

Question 2

if we have a Transformation T: V->W is map from V to W
What is its domain:
What is its codomain:
What it is the image of V:
What it is the range of T:

Answer 2

Domain: The space V
Codomain: The space W
The image of V: for each vector v E V, the image is called T(v)
The range of T: is the set of all images T(v)-or T(V)

Question 3

if T: [a] -> [a]
[b] [0]
What is its domain:
What is its codomain:
What it is the image of V:
What it is the range of T:

Answer 3

Transformation: 2D -> 2D
Domain: 2D
Codomain: 2D
Range of T: 1D(x-axis)

Question 4

How can be proved that T: V -> W is a L.T

Answer 4

1. T(u+v) = T(u) + T(v)
2. T(λ.u) = λT (u)

Question 5

Can we compose L.T and get another L.T

Answer 5

Yes