Q5. Let T: R"→→R" be a linear map. Prove that the following are equivalent: (i) T is injective. (ii) For all vectors 7₁,

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Q5. Let T: R"→→R" be a linear map. Prove that the following are equivalent: (i) T is injective. (ii) For all vectors 7₁,

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Q5 Let T R R Be A Linear Map Prove That The Following Are Equivalent I T Is Injective Ii For All Vectors 7 1
Q5 Let T R R Be A Linear Map Prove That The Following Are Equivalent I T Is Injective Ii For All Vectors 7 1 (12.5 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 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.
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