Week 12

Question 1

What qualities does a linear transformation ave?

Answer 1

• T(v1) + T(v2) = T(v1 + v2)
  -T(αu) = αT(u)

Question 2

2 linear transformations?

Answer 2

• empty circle
  -(S ◦T)(v) = (ST)(v) = S(T(v))

Question 3

Range?

Answer 3

R(T) = {w ∈W |w=T(v) for some v ∈V}⊆W.

Question 4

Kernel?

Answer 4

ker(T) = {v ∈ V | T(v) = 0} ⊆ V
0 is the zero vector

Question 5

For matrix what is kernel?

Answer 5

Null Space

Question 6

For a linear transformation where T(x) = A(x) what is range?

Answer 6

CS (A)

Question 7

For a linear transformation where T(x) = A(x) what is kernel?

Answer 7

N(A)

Question 8

Rank nulity theorem for linear kernel and range?

Answer 8

dim(R(T)) +dim(ker(T)) = n

where n is columns