Problem 6

(1 point) Suppose f(en) = an for n = 1, 2 and f is a linear transformation. y 3 e2 -1 -1 -2 -24 a1 -3 -2 -1 -3 2 3 -3 -2 -1 a2 3 Domain Codomain a. f : IRk -> R" for k = and n = b. The set of vectors { e1, e2} is (select all that apply): O A. linearly independent OB. a basis for the domain OC. a basis for the codomain D. a spanning set E. none of these c. The set of vectors { f(e1 ), f(e2) } is (select all that apply): O A. a basis for the domain OB. a basis for the codomain OC. linearly independent D. a spanning set DE. none of these d. The linear transformation f is (select all that apply): A. surjective (onto) B. injective (one-to-one) OC. bijective (an isomorphism) D. none of these e. Using that f is a linear transformation, find f(-2e, + 3e2). Enter your answer as a coordinate vector such as . f(-2e1 + 3e2) = f. Find the matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x) = Ax. For instance, enter [ [1,2], [3,4] ] for the matrix 3 2] A =