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Introduction to Linear Algebra

Exercise 3.1.3

Answers

(a): $cx$ may not be in our set: not closed under multiplication. Also no 0 and no $- x$ .
(b): $c (x + y)$ is the usual ${(xy)}^{c}$ , while $c x + c y$ is the usual $(x^{c}) (y^{c}) .$ Those are equal. With $c = 3, x = 2, y = 1$ this is $3 (2 + 1) = 8$ . The zero vector is the number 1.

mathchakra

2022-01-16 13:16

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