The question was rejected with the claim that it is incomplete. The question was asked by one of the most reputed institute in India. The correct answer as provided by the insititute that asked the question is C for 35 and B for 36. I assure the question is more than complete.If you still feel that the question is incomplete, please provide me more details and I will complete the question and post it over. The following information is used in the next Two questions. Consider a linear transforma-tionP: R" → R". Let R(P) = {Px | x e R"} and N (P) = {x € R" | Px = 0}.P is said to be a projector if(a) every r e R" can be uniquely written as r = y +z for some y e R(P) and z E N (P),and(b) P(y + z) = y for all y € R(P) and z EN (P)35. If P is a projector, thenA. P² = I, where I is the identity mappingВ. Р— Р-1C. P2 = PD. Both (a) and (b)36. If P is a projector and Q : R" → R" is a linear transformation such that R(P) = R(Q),thenА. QP — PВ. РО — QC. QP = ID. PQ = I

Answered: Image /qna-images/answer/b2b766c5-1ddf-418f-8117-de641d88df62.jpg

The following information is used in the next Two questions. Consider a linear transforma- tion P : R" → R". Let R(P) = {Px | x € R"} and N (P) = {r € R" | Px = 0}. P is said to be a projector if (a) every r € R" can be uniquely written as r = y+ z for some y e R(P) and z € N(P), and (b) P(y + z) = y for all y e R(P) and z E N(P) 35. If P is a projector, then A. P² = I, where I is the identity mapping В. Р3 Р-1 C. P2 = P D. Both (a) and (b) 36. If P is a projector and Q : R™ → R" is a linear transformation such that R(P) = R(Q), then А. QP3D P В. РQ 3 Q C. QP = I D. PQ = I