1. (10 points) True/False questions. No justification necessary. (a) True False If the linear transformation T : P1 - P1 has matrix IT]a = with respect to the standard basis a = {x, 1}, then T(ax + b) = bac + a . (b) True False If w(y1, yz, y3, y4) = -4 on (0, 1), then y1, yz, y3, y4 are linearly in- dependent in F(0, 1). (c) True False dim ( MAX3 (IR) ) = 7. (d) True False If D is the derivative operator, then nullity(D) = 1. (e) True False The set of solutions of the differential equation y(4 ) +y (3 ) + y " + y ' ty = 0 , is a vector space of dimension 4. (f) True False If v E R" and a is the standard basis of R", then [ula = v. g) True False If T : V - W is a linear transformation, then the ker(T) is a subspace of W. h) True False If T : V - W is a linear transformation, then the im(T) is a subspace of V. (i) True False If T is an operator on P2 of rank 2, then nullity(T) = 0. (j) True False If V is a vector space and v is any vector in V, then {v } is a linearly independent set of vectors