Q5. Let T: R"→→R" be a linear map. Prove that the following are equivalent: (i) T is injective. (ii) For all vectors 7₁,
Posted: Wed Jul 06, 2022 11:50 am
Q5. Let T: R"→→R" be a linear map. Prove that the following are equivalent: (i) T is injective. (ii) For all vectors 7₁, 72,..., ER", if the set (71, 72,..., 7) CR" is linearly inde- pendent, then the corresponding set {T(₁),T(7₂).....T(7)} CR is also linearly independent.