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Posted: **Fri Jul 08, 2022 5:32 am**

: Let T R R Be A Linear Map Prove That The Following Are Equivalent I T Is Injective Ii For All Vectors V1 V2 1 (19.64 KiB) Viewed 25 times

Let T: R" → R™ be a linear map. Prove that the following are equivalent: (i) T is injective. (ii) For all vectors V1, V2,..., VER", if the set {1, 2,..., Uk} CR" is linearly inde- pendent, then the corresponding set {T(7₁), T(7₂),.. ‚T(7k)} C R™ is also linearly independent.