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Complete the proof of the remaining property of this theorem by supplying the justification for each step. Use the properties of vector addition and scalar multiplication from this theorem. If cv = 0, then c = 0 or v = 0. If c = 0, then you are done. If c + 0, then c-1 exists, and you have the following. c-(cv) = c-1o c-(cv) = 0 (c-lc)v = 0 1v = 0 v = 0 (a) c-(cv) = c-10 O apply the distributive property O apply the property a0 = 0 for any scalar a O apply the associative property of addition O apply the multiplicative identity property O multiply both sides of the equation by a non-zero constant (b) c-1(cv) = 0 O apply the distributive property O multiply both sides of the equation by a non-zero constant O apply properties of real numbers O apply the property a0 = 0 for any scalar a O apply the multiplicative identity property (c) (c-lc)v = 0 O apply the multiplicative identity property O multiply both sides of the equation by a non-zero constant O apply the distributive property O apply the associative property of multiplication O apply the property a0 = 0 for any scalar a (d) 1v = 0 O apply the property a0 = 0 for any scalar a O the product of multiplicative inverses is 1 O apply the additive inverse property O apply the multiplicative identity property O apply the distributive property

Complete the proof of the remaining property of this theorem by supplying the justification for each step. Use the properties of vector addition and scalar multiplication from this theorem. If cv = 0, then c = 0 or v = 0. If c = 0, then you are done. If c + 0, then c-1 exists, and you have the following. c-(cv) = c-1o c-(cv) = 0 (c-lc)v = 0 1v = 0 v = 0 (a) c-(cv) = c-10 O apply the distributive property O apply the property a0 = 0 for any scalar a O apply the associative property of addition O apply the multiplicative identity property O multiply both sides of the equation by a non-zero constant (b) c-1(cv) = 0 O apply the distributive property O multiply both sides of the equation by a non-zero constant O apply properties of real numbers O apply the property a0 = 0 for any scalar a O apply the multiplicative identity property (c) (c-lc)v = 0 O apply the multiplicative identity property O multiply both sides of the equation by a non-zero constant O apply the distributive property O apply the associative property of multiplication O apply the property a0 = 0 for any scalar a (d) 1v = 0 O apply the property a0 = 0 for any scalar a O the product of multiplicative inverses is 1 O apply the additive inverse property O apply the multiplicative identity property O apply the distributive property

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(e) v = 0 apply properties of real numbers apply the additive inverse property apply the associative property of multiplication apply the multiplicative identity property apply the distributive property
Transcribed Image Text:(e) v = 0 apply properties of real numbers apply the additive inverse property apply the associative property of multiplication apply the multiplicative identity property apply the distributive property
Complete the proof of the remaining property of this theorem by supplying the justification for each step. Use the properties of vector addition and scalar multiplication from this theorem. If cv = 0, then c = 0 or v = 0. If c = 0, then you are done. If c + 0, then c¯1 exists, and you have the following. c-1(cv) = c-10 c-1(cv) (c-!c)v 1v = 0 V = 0 (a) c-1(cv) = c-10 apply the distributive property apply the property a0 = 0 for any scalar a apply the associative property of addition apply the multiplicative identity property multiply both sides of the equation by a non-zero constant (b) c-1(cv) = 0 apply the distributive property multiply both sides of the equation by a non-zero constant apply properties of real numbers apply the property a0 = 0 for any scalar a apply the multiplicative identity property (c) (c-!c)v = 0 apply the multiplicative identity property multiply both sides of the equation by a non-zero constant apply the distributive property apply the associative property of multiplication apply the property a0 = O for any scalar a (d) 1v = 0 apply the property a0 = 0 for any scalar a the product of multiplicative inverses is 1 apply the additive inverse property apply the multiplicative identity property apply the distributive property O O O O
Transcribed Image Text:Complete the proof of the remaining property of this theorem by supplying the justification for each step. Use the properties of vector addition and scalar multiplication from this theorem. If cv = 0, then c = 0 or v = 0. If c = 0, then you are done. If c + 0, then c¯1 exists, and you have the following. c-1(cv) = c-10 c-1(cv) (c-!c)v 1v = 0 V = 0 (a) c-1(cv) = c-10 apply the distributive property apply the property a0 = 0 for any scalar a apply the associative property of addition apply the multiplicative identity property multiply both sides of the equation by a non-zero constant (b) c-1(cv) = 0 apply the distributive property multiply both sides of the equation by a non-zero constant apply properties of real numbers apply the property a0 = 0 for any scalar a apply the multiplicative identity property (c) (c-!c)v = 0 apply the multiplicative identity property multiply both sides of the equation by a non-zero constant apply the distributive property apply the associative property of multiplication apply the property a0 = O for any scalar a (d) 1v = 0 apply the property a0 = 0 for any scalar a the product of multiplicative inverses is 1 apply the additive inverse property apply the multiplicative identity property apply the distributive property O O O O
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