9. Linear Transformations 2

Question 1

Kernal of F Linear Transformation

Answer 1

Let T:V->W, the kernel of T is the set of all vectors in V that are mapped by T to 0 in W.

Question 2

Range of F Linear Transformation

Answer 2

The range is the set of all vectors in W that are images of vectors in V under T

Question 3

Properties of Range and Kernal for Transformations

Answer 3

The Kernel is a subspace of V where the range is a subspace of W.

Question 4

Rank of Transformation

Answer 4

The dimension of range

Question 5

Nullity of Transformation

Answer 5

Dimension of Kernel

Question 6

Rank-Nullity Theorem

Answer 6

rank(T) + nullity(T) = dim(V)

Question 7

Injective Linear Transformation

Answer 7

Ker(T)=0

Question 8

Invertible Linear Transformation

Answer 8

Only if it is bijective

Question 9

Isomorphic Linear Transformation

Answer 9

Only if it is bijective

Question 10

If Dim(V)=Dim(W)

Answer 10

The two linear transformations are isomorphic to each other.

Question 11

Matrix for Linear Transformations

Answer 11

Every linear transformation between finite dimensional vector spaces can be shown as a matrix