Question: Consider M2x2(C) as a real vector space (i.e., A ( R). Let T : M2x2(C) - M2x2(C) be given by a, b, c, dec where

Consider M2x2(C) as a real vector space (i.e., A ( R). Let T : M2x2(C) - M2x2(C) be given by a, b, c, dec where a denotes the complex conjugate of a. (A) Prove that T is a linear transformation of real vector space. (B) Find a basis for null(7). Is T injective? (C) Find a basis for range(T). Is T surjective? (D) Find a matrix M(T) which represents T. (E) If we instead consider M2x2(C) as a complex vector space (i.e., A e C), is T a linear transforma- tion? Justify your

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