Let A be an mxn matrix, and let B and C have sizes for which the indicated sums and products are defined. Prove that A(B and that (B+C)A = BA + CA. Use the row-column rule. The (ij)-entry in A(B+C) can be written in either of the two ways bel a₁1 (b₁j + C1j) +...+ain (Dnj + Cnj) or n Σaik (bki + Cki) k=1 Prove that A(B+C) = AB + AC. Choose the correct answer below. n O A. a The (ij)-entry of A(B+C) equals the (ij)-entry of AB + AC, because Σaik (bki + Cki) = Σaikki - Σ ªik kj k=1 k=1 k=1 B. The (ij)-entry of A(B+C) equals the (ij)-entry of AB + AC, because aik (bj + Ckj) = Σ ªikºkj k=1 k=1 + n Σaikki k=1 O C. The (ij)-entry of A(B+C) equals the (ij)-entry of AB + AC, because Σaik (bki + Cki) = Σ akibjk - + • Σ ou (tu * 54 ) = Σ Buty - Ė Puser Sakisk k=1 k=1 k=1

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