11. Let V be a vector space and T a linear transformation from V into V. Prove that the following two statements about T are equivalent. (a) The intersection of the range of T and the null space of T is the zero subspace of V. (b) If T(Ta) =0, then Ta = 0.

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Q: Prove that.

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A: formula used  xa×xb=xa+blet  A=12x4y8z74xy3z2

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A: Given:2cos 50+sin 506

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A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

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A: We prove the given argument by using rules of inference.