www.bbcnoun.com.ng MTH212_22 TMA 2; 10/10 1. Let U, V be vector spaces of dimensions m and n, respectively. Suppose W is a subspace of V of dimension p (≤n). Let X = {T∈ L(U, V): T(u) ∈W for all u in U}. .Find the dimension of L(U, V) mp 2. Two finite – dimensional vector spaces U and V are isomorphic if and only if Dim U = Dim V 3. Let U and V be vector spaces over a field F and dim U = n. Let T:U→V be a linear operator. What is rank (T) + nullity (T)? n 4. Linear transformation are also called ___ Vector space homomorphism 5. Let I: V→ V be the identity transformation. What is Ker I? O 6. The ___ of T is defined to be the dimension of R(T), the range space of T. Rank 7. Let T: U→ V be a linear transformation. T is called ___ if, for u1,u2∈U with u1=u2, we have T (u1)= T (u2) Injective 8. Let L:R3→R be the map given by L(x,y,z) = x + y + z. What is nullity (L)? 2 9. Let T:V→V be a linear transformation and let {e1, …, en} be a basis of V. Then T is one-one and onto if and only if {T (e1), …, T(en)} is ___ Linear independent 10. Let T: R3→R be defined by T(x1, x2,x3) = 3x1 +x2 + 2x3 What is R(T)? The whole real line R.