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Exercise 1.2.21

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$2 v \cdot w \leq 2 ∥ v ∥ ∥ w ∥$ leads to $∥ v + w ∥^{2} = v \cdot v + 2 v \cdot w + w \cdot w \leq ∥ v ∥^{2} + 2 ∥ v ∥ ∥ w ∥ +$ $∥ w ∥^{2} .$ This is ${(∥ v ∥ + ∥ w ∥)}^{2} .$ Taking square roots gives $∥ v + w ∥ \leq ∥ v ∥ + ∥ w ∥$

mathchakra

2021-11-20 14:07

Exercise 1.2.21

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