Question: Let A = [a] be a 2 2 matrix, B = [bij] a 2 2 matrix, and C = [Cij] a 3 x 2

Let A = [a] be a 2 2 matrix, B = [bij]

Let A = [a] be a 2 2 matrix, B = [bij] a 2 2 matrix, and C = [Cij] a 3 x 2 matrix. (a) Does the matrix D = [dij] = A + B exist? If so, what is its size and what is d22 in terms of the entries of A and B? If not, why not? (b) Does the matrix E = [ej] = AB exist? If so, what is its size and what is e12 in terms of the entries of A and B? If not, why not? (c) Does the matrix F = [fij] = BC exist? If so, what is its size and what is f12 in terms of the entries of B and C? If not, why not? (d) Does the matrix G = [gij] = CA exist? If so, what is its size and what is 912 in terms of the entries of C and A? If not, why not? (e) Does the matrix H = [hij] = CBA exist? If so, what is its size and what is h21 in terms of the entries of A, B, and C? If not, why not?

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