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Exercise 1.2.19

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Start from the rules $(1), (2), (3)$ for $v \cdot w = w \cdot v$ and $u \cdot (v + w)$ and $(cv) \cdot w$ . Use nule $(2)$ for $(v + w) \cdot (v + w) = (v + w) \cdot v + (v + w) \cdot w .$ By rule $(1)$ this is $v \cdot (v + w) + w \cdot (v + w) .$ Rule (2) again gives $v \cdot v + v \cdot w + w \cdot v + w \cdot w =$ $v \cdot v + 2 v \cdot w + w \cdot w .$ Notice $v \cdot w = w \cdot v!$ The main point is to feel free to open up parentheses.

mathchakra

2021-11-20 14:06

Exercise 1.2.19

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