Page 345 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

THEOREM 5.1.1

Let V be a vector space, u a vector in V, and k a scalar; then:
(a)

(b)

(c)

(d) If , then or .

We shall prove parts (a) and (c) and leave proofs of the remaining parts as exercises.

Proof (a) We can write

By Axiom 5 the vector has a negative, . Adding this negative to both sides above yields
or

Proof (c) To show that , we must demonstrate that . To see this, observe that

Exercise Set 5.1

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