www.bbcnoun.com.ng MTH212 8/10 1. __________ is the study of certain mappings between two vector spaces. Select one: Zero transformation Linear transformations (ANS) Identity transformation Relation 2. he range of T, denoted by R(T), is the set ___ Select one: {T(x):x ∈ T} {x∈U: T(x) = 0 } {T(x):x ∈ U} (ANS) {x∈U: T(x) } 3. e1 = (1,0,0),e2 = (0, 1, 0) and e3= (0, 0, 1) form the standard basis of R3. Let (1,2), (2,3) and (3,4) be three vectors in R2. The linear transformation T: R3→ R2 such that T(e1) = (1,2), T(e2) = (2,3) and T(e3) = (3,4) is given as ___ Select one: (x1 +2x2 + 3x3, 2x1 + 4x3 (2x1 +2x2 + 3x3, x1 + 4x3) (x1 +2x2 , 2x3 + 3x2 + 4x3) (x1 +2x2 + 3x3, 2x1 + 3x2 + 4x3) (ANS) 4. Let U be a given vector over F. Then L(U,F) is called the ___ space of U* and is denoted by U. Select one: identity dual (ANS) null inverse 5. Consider the vector space U over a field F, and the function T:U→U defined by T(u) = u for all u ∈ U. This transformation is called the ___ Select one: Linear transformations Relation Zero transformation Identity transformation (ANS) 6. Let I: V→ V be the identity transformation. What is R(I)? Select one: 0 (ANS) {x∈U:T(x) = 0 } V x∈U: T(x) } 7. Let T: U→V be defined by T(u) = 0 for all u∈U. This transformation is called the ___________ Select one: Linear transformations (ANS) Zero transformation Relation Identity transformation 8. The kernel (or null space) of T, denoted by Ker T, is the set Select one: {x∈U: T(x) = 0 } (ANS) {T(x):x ∈ T} {x∈U:T(x) } {T(x):x ∈ U} 9. Let U and V be vector spaces over a field F. A ___ from U to V is a function T: U→V, such that T(u1 + u2) = T(u1) + T(u2), for u1, u2 ∈U, and T(αu) = αT(u) for α∈ F and U ∈ U. Select one: Identity transformation Relation Linear transformations (ANS) Zero transformation 10. The complex field C is a ___ over R Select one: null space vector space (ANS) complex space eigen space