Exercise 3.C.11

Answers

Proof. We have

\begin{aligned} (aC)_1, k & = \sum_{r = 1}^{n} a_{1, r} C_{r, k} \\ = \sum_{r = 1}^{n} a_{r} C_{r, k} \\ = a_{1} C_{1, k} + \dots + a_{n} C_{n, k} \\ = a_{1} (C_{1, .})_1, k + \dots + a_{n} (C_{n, .})_1, k \\ = (a_{1} C_{1, .} + \dots + a_{n} C_{n, .})_1, k \end{aligned}

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2017-10-06 00:00