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Introduction to Linear Algebra

Exercise 1.2.4

Answers

(a) $v \cdot (- v) = - 1$

(b) notice $v \cdot w = w \cdot v$ :

\begin{array}{l} (v + w) \cdot (v - w) & = v \cdot v + w \cdot v - v \cdot w - w \cdot w \\ = 1 + () - () - 1 = 0 \end{array}

So, $𝜃 = 9 0^{∘}$ .

(c) $(v - 2 w) \cdot (v + 2 w) =$ $v \cdot v - 4 w \cdot w = 1 - 4 = - 3$

mathchakra

2021-11-20 14:00

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