Exercise 2.2

Question

The Pythagorean theorem asserts that for a set of $n$ orthogonal vectors $\{x_i\}$,
$$\left\|\sum_{i=1}^{n}x_iight\|^2 = \sum_{i=1}^{n} \|x_i\|^2.$$
(a) Prove this in the case $n = 2$ by an explicit computation of $\|x_1+x_2\|^2$.
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(b) Show that this computation also establishes the general case, by induction.

Desh Raj · Accepted Answer

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Exercise 2.2

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Exercise 2.2

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