Let V be an inner product space. Then for x, y, z ∈V and c ∈F, the following statements are true. (a) <x, y + z>= <x,y>+<x,z> . (b) <x,cy>=c . (c) <x, 0>= <0, x>= 0. (d) <x,x> = 0 if and only if x = 0 . (e) <x, y>= <x, z>for all x ∈V, then y = z.

Let V be an inner product space. Then for x, y, z ∈V and c ∈F, the following statements are true. (a) <x, y + z>= <x,y>+<x,z> . (b) <x,cy>=c . (c) <x, 0>= <0, x>= 0. (d) <x,x> = 0 if and only if x = 0 . (e) <x, y>= <x, z>for all x ∈V, then y = z.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 6TFE: True or False Label each of the following statements as either true or false. 6. Every bijection is...

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Question

Let V be an inner product space. Then for x, y, z ∈V and c ∈F, the following statements are true.

(a) <x, y + z>= <x,y>+<x,z> .

(b) <x,cy>=c .

(d) <x,x> = 0 if and only if x = 0 .

(e) <x, y>= <x, z>for all x ∈V, then y = z.

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