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Complete the proof of Property 4 of the following theorem by supplying the justification for each step. Properties of Additive Identity and Additive Inverse Let v be a vector in R", and let c be a scalar. Then the properties below are true. 1. The additive identity is unique. That is, if v + u = v, then u = 0. 2. The additive inverse of v is unique. That is, if v + u = 0, then u = -v. 3. Ov - 0 4. co - 0 5. If cv - 0, then c- 0 or v = 0. 6. -(-v) = v Use the properties of vector addition and scalar multiplication from the following theorem. Properties of Vector Addition and Scalar Multiplication in R" Let u, v, and w be vectors in R", and let c and d be scalars. 1. u+ v is a vector in R". Closure under addition 2. u+ v-v+ u 3. (u + u) + w = u+ (u + w) 4. u +0 =u 5. u + (-u) - 0 6. cu is a vector in R". 7. c(u + v) = cu + v 8. (c + d)u - cu + du 9. c(du) - (cd)u 10. 1(u) - u Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property Step Justification c0 = c(0 + 0) -Select--- co - c0 + co Select- cô + (-c0) = (c0 + co) + (-c0) -Select-- 0 = (c0 + c0) + (-c0) 0 = c0 + (c0 + (-co)) Select -Select-- 0 - c0 +0 Select--- 0- c0 Select--

Complete the proof of Property 4 of the following theorem by supplying the justification for each step. Properties of Additive Identity and Additive Inverse Let v be a vector in R", and let c be a scalar. Then the properties below are true. 1. The additive identity is unique. That is, if v + u = v, then u = 0. 2. The additive inverse of v is unique. That is, if v + u = 0, then u = -v. 3. Ov - 0 4. co - 0 5. If cv - 0, then c- 0 or v = 0. 6. -(-v) = v Use the properties of vector addition and scalar multiplication from the following theorem. Properties of Vector Addition and Scalar Multiplication in R" Let u, v, and w be vectors in R", and let c and d be scalars. 1. u+ v is a vector in R". Closure under addition 2. u+ v-v+ u 3. (u + u) + w = u+ (u + w) 4. u +0 =u 5. u + (-u) - 0 6. cu is a vector in R". 7. c(u + v) = cu + v 8. (c + d)u - cu + du 9. c(du) - (cd)u 10. 1(u) - u Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property Step Justification c0 = c(0 + 0) -Select--- co - c0 + co Select- cô + (-c0) = (c0 + co) + (-c0) -Select-- 0 = (c0 + c0) + (-c0) 0 = c0 + (c0 + (-co)) Select -Select-- 0 - c0 +0 Select--- 0- c0 Select--

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.1: Vector In R^n
Problem 61E: Illustrate properties 110 of Theorem 4.2 for u=(2,1,3,6), v=(1,4,0,1), w=(3,0,2,0), c=5, and d=2....
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can you please help me with this problem? the 2nd pic is the choices. Thank you, I'll rate if you gave me the correct answer.
|---Select--- -Select-- additive identity property associative property of addition commutative property of addition multiplicative identity property distributive property | add -c0 to both sides additive inverse property |associative property of multiplication
Transcribed Image Text:|---Select--- -Select-- additive identity property associative property of addition commutative property of addition multiplicative identity property distributive property | add -c0 to both sides additive inverse property |associative property of multiplication
Complete the proof of Property 4 of the following theorem by supplying the justification for each step. Properties of Additive Identity and Additive Inverse Let v be a vector in R", and let c be a scalar. Then the properties below are true. 1. The additive identity is unique. That is, if v + u = v, then u = 0. 2. The additive inverse of v is unique. That is, if v + u = 0, then u = -v. 3. Ov = 0 4. co = 0 5. If cv = 0, then c= 0 or v= 0. 6. -(-v) = v Use the properties of vector addition and scalar multiplication from the following theorem. Properties of Vector Addition and Scalar Multiplication in R" Let u, v, and w be vectors in R", and let c and d be scalars. 1. u + v is a vector in R". 2. u + v = v + u 3. (u + u) + w =u + (u + w) 4. u + 0 = u 5. u + (-u) = 0 Closure under addition 6. cu is a vector in R". 7. c(u + v) = cu + cv 8. (c + d)u = cu + du 9. c(du) = (cd)u 10. 1(u) = u Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property Step Justification c0 = c(0 + 0) --Select-- c0 - c0 + c0 -Select-- c0 + (-c0) = (c0 + c0) + (-c0) Select-- %3D 0 = (c0 + c0) + (-c0) -Select- 0 = c0 + (c0 + (-c0)) --Select-- - 0 = c0 + 0 -Select--- 0 = c0 - Select---
Transcribed Image Text:Complete the proof of Property 4 of the following theorem by supplying the justification for each step. Properties of Additive Identity and Additive Inverse Let v be a vector in R", and let c be a scalar. Then the properties below are true. 1. The additive identity is unique. That is, if v + u = v, then u = 0. 2. The additive inverse of v is unique. That is, if v + u = 0, then u = -v. 3. Ov = 0 4. co = 0 5. If cv = 0, then c= 0 or v= 0. 6. -(-v) = v Use the properties of vector addition and scalar multiplication from the following theorem. Properties of Vector Addition and Scalar Multiplication in R" Let u, v, and w be vectors in R", and let c and d be scalars. 1. u + v is a vector in R". 2. u + v = v + u 3. (u + u) + w =u + (u + w) 4. u + 0 = u 5. u + (-u) = 0 Closure under addition 6. cu is a vector in R". 7. c(u + v) = cu + cv 8. (c + d)u = cu + du 9. c(du) = (cd)u 10. 1(u) = u Commutative property of addition Associative property of addition Additive identity property Additive inverse property Closure under scalar multiplication Distributive property Distributive property Associative property of multiplication Multiplicative identity property Step Justification c0 = c(0 + 0) --Select-- c0 - c0 + c0 -Select-- c0 + (-c0) = (c0 + c0) + (-c0) Select-- %3D 0 = (c0 + c0) + (-c0) -Select- 0 = c0 + (c0 + (-c0)) --Select-- - 0 = c0 + 0 -Select--- 0 = c0 - Select---
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