Question

Mnxn (m). (3) Let U and V be vector spaces. Let Hom(U, V) denote the set of linear transformations from U to V. Note that Hom(U, V) is a subset of the vector space Fun(U, V), the set of functions from U to V (you don't need to check this). Show that Hom(U, V) is a subspace of Fun (U, V).

          Mnxn (m).
(3) Let U and V be vector spaces. Let Hom(U, V) denote the set of linear transformations
from U to V. Note that Hom(U, V) is a subset of the vector space Fun(U, V), the set of
functions from U to V (you don't need to check this). Show that Hom(U, V) is a subspace
of Fun (U, V).

Mnxn (m).
(3) Let U and V be vector spaces. Let Hom(U, V) denote the set of linear transformations
from U to V. Note that Hom(U, V) is a subset of the vector space Fun(U, V), the set of
functions from U to V (you don't need to check this). Show that Hom(U, V) is a subspace
of Fun (U, V).

Added by Lauren G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

06/08/2022

Step 1

Since the zero transformation maps every vector in U to the zero vector in V, it is a linear transformation. Therefore, the zero transformation is in Hom(U,V). Show more…

Show all steps

Thanks for your feedback!

(3) Let U and V be vector spaces. Let Hom(U,V) denote the set of linear transformations from U to V. Note that Hom(U,V) is a subset of the vector space Fun(U,V), the set of functions from U to V (you don't need to check this). Show that Hom(U,V) is a subspace of Fun(U,V).