(b) Let

T_(1):R^(5)->R^(3)

and

T_(2):R^(3)->R^(2)

be linear maps.\ i. What are the possible dimensions for the kernel of

T_(2)

? For each possibility find an example.\ ii. If

dim(ker(T_(2)))=3

, what is

dim(ker(T_(2)@T_(1)))

?\ iii. If

T_(1)

is surjective, what is

dim(ker(T_(1)))

?

(b) Let T1:R5R3 and T2:R3R2 be linear maps. i. What are the possible dimensions for the kernel of T2 ? For each possibility find an example. ii. If dim(ker(T2))=3, what is dim(ker(T2T1)) ? iii. If T1 is surjective, what is dim(ker(T1))