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3. Let T: R2*2 _> R2*2 be the mapping defined by T(A) = A + A - tr(A)I for the 2-by-2 matrix A, where tr(

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3. Let T: R2*2 _> R2*2 be the mapping defined by T(A) = A + A" - tr(A)I for the 2-by-2 matrix A, where tr( A) is the trace of A and I is the 2-by-2 identity matrix. (a) Find the matrix of T with respect to the standard basis of IR2x2 (b) Calculate the rank and nullity of T', and give bases for the image and kernel of T

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