Exercise 6.A.12

Answers

Proof. Take $x = (x_{1}, \dots, x_{n})$ and $y = (1, \dots, 1)$ ( $n$ ones). By 6.15, we have

| x_{1} + \dots + x_{n} | = | ⟨ x, y ⟩ | \leq | | x | | | | y | | = \sqrt{n} \sqrt{x_{1}^{2} + \dots + x_{n}^{2}}

Squaring each side now gives the desired result. □

celiopassos

2017-10-06 00:00