Linear Algebra 1

Question 1

what conditions must a linear map T satisfy

Answer 1

T(v1 + v2) = T(v1) + Y(v2)
T(av1) = a * T(v1), where a is a scalar

Question 2

True or False: If T and S are both linear maps, is T + S linear?

Answer 2

True

Question 3

True or False: If T is a linear map, is a * T also a linear map, where a is a scalar

Answer 3

True

Question 4

True or False: is the composition of S and T also linear

Answer 4

True: (SoT) is linear

Question 5

Give an alternative notation for the composition of T with S (ToS)

Answer 5

TS