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4. (Quiz 9) Let M2x2 be the vector space of all 2x2 matrices. Define T M2x2 M2x2 3a b + 2c by T(A) = A+ 2AT . For example; if A = then T(A) 26 + c 3d Prove that T is a linear transformation. Find basis for the range of T. iii Find a basis for the kernel of T.

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