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Posted: **Wed Jul 06, 2022 12:38 pm**

: Q5 Let T R R Be A Linear Map Prove That The Following Are Equivalent I T Is Injective Ii For All Vectors V1 1 (21.3 KiB) Viewed 13 times

Q5. Let T: R → R" be a linear map. Prove that the following are equivalent: (i) T is injective. (ii) For all vectors V1, V2,..., k € R", if the set {1, 2,..., Uk} CR" is linearly inde- pendent, then the corresponding set {T(7₁),T(7₂),..., T(Uk)} R™ is also linearly independent.