Given linear mapping T:V->W and v₁ ,v₂,dots,v_(n)inV . If {T(v₁),T(v₂),dots,T(vn)} is linearly independent, indicate that {v₁,v₂,dots,vn} are also linearly-independent. Explain why the statement converter above doesn't always apply. What are the conditions required for the converter to take effect?

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04-06-2024
Mathematics

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Given linear mapping T:V->W and v₁ ,v₂,dots,v_(n)inV . If {T(v₁),T(v₂),dots,T(vn)} is linearly independent, indicate that {v₁,v₂,dots,vn} are also linearly-independent. Explain why the statement converter above doesn't always apply. What are the conditions required for the converter to take effect?

Sagot :

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