Suppose u₁ and u2 both have the property of being an additive inverse of v. That is, for this arbitra particular vector v, u₁ + v = 0 and u₂ + v= 0. Supply a reason for each line of the string of equ proving that u₁ = u₂, thus proving that additive inverses are unique [and therefore -1 v is the ad inverse of v]. U₁=U₁+0 = U₁ + (u₂ + v) = U₁ + (v + U₂) (U₁ + v) + U₂ = = 0 + U₂ Select an answer [Select an answer Select an answer Select an answer Select an answer Soloct on answor
Suppose u₁ and u2 both have the property of being an additive inverse of v. That is, for this arbitra particular vector v, u₁ + v = 0 and u₂ + v= 0. Supply a reason for each line of the string of equ proving that u₁ = u₂, thus proving that additive inverses are unique [and therefore -1 v is the ad inverse of v]. U₁=U₁+0 = U₁ + (u₂ + v) = U₁ + (v + U₂) (U₁ + v) + U₂ = = 0 + U₂ Select an answer [Select an answer Select an answer Select an answer Select an answer Soloct on answor
Transcribed Image Text:Suppose ₁ and ₂ both have the property of being an additive inverse of v. That is, for this arbitrary but
particular vector v, u₁ + v = 0 and u₂ + v = 0. Supply a reason for each line of the string of equalities
proving that u₁ = u₂, thus proving that additive inverses are unique [and therefore -1 v is the additive
inverse of v].
Select an answer
= U₁ + (U₂ + v)
Select an answer
= U₁ + (v + U₂) [Select an answer
= (U₁ + v) + U₂
Select an answer
= 0 + U₂
Select an answer
Select an answer
= U2
U₁ = U₁ + 0
Transcribed Image Text:Suppose u₁ and u₂ both have the property of being an additive inverse of v. That is, for this arbitrary but
particular vector v, u₁ + v = 0 and u₂ + v= 0. Supply a reason for each line of the string of equalities
proving that u₁ = U₂, thus proving that additive inverses are unique [and therefore -1 v is the additive
inverse of v].
U₁ = U₁ + 0
= U₁ + (U₂ + v)
= U₁ + (v + U₂)
(U₁ + v) + U₂
= 0 + U₂
= U12
=
Check Answer
✓ Select an answer
assumption of the claim
vector space property 1: closure under addition
vector space property 2: vector addition is commutative
vector space property 3: vector addition is associative
vector space property 4: property of the additive identity
vector space property 5: existence of additive inverses
vector space property 6: closure under scalar multiplication
vector space property 7: property of the multiplicative identity, 1
vector space property 8: distribution of scalars over vectors
vector space property 9: distribution of vectors over scalars
vector space property 10: associativity of scalar multiplication
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![Suppose ₁ and ₂ both have the property of being an additive inverse of v. That is, for this arbitrary but
particular vector v, u₁ + v = 0 and u₂ + v = 0. Supply a reason for each line of the string of equalities
proving that u₁ = u₂, thus proving that additive inverses are unique [and therefore -1 v is the additive
inverse of v].
Select an answer
= U₁ + (U₂ + v)
Select an answer
= U₁ + (v + U₂) [Select an answer
= (U₁ + v) + U₂
Select an answer
= 0 + U₂
Select an answer
Select an answer
= U2
U₁ = U₁ + 0](https://content.bartleby.com/qna-images/question/ad61a16a-ccb3-4100-87e8-33e1dead9976/bda4cdbb-a4ba-4b52-8697-5d5efd397c95/t8ct1h_processed.png)
![Suppose u₁ and u₂ both have the property of being an additive inverse of v. That is, for this arbitrary but
particular vector v, u₁ + v = 0 and u₂ + v= 0. Supply a reason for each line of the string of equalities
proving that u₁ = U₂, thus proving that additive inverses are unique [and therefore -1 v is the additive
inverse of v].
U₁ = U₁ + 0
= U₁ + (U₂ + v)
= U₁ + (v + U₂)
(U₁ + v) + U₂
= 0 + U₂
= U12
=
Check Answer
✓ Select an answer
assumption of the claim
vector space property 1: closure under addition
vector space property 2: vector addition is commutative
vector space property 3: vector addition is associative
vector space property 4: property of the additive identity
vector space property 5: existence of additive inverses
vector space property 6: closure under scalar multiplication
vector space property 7: property of the multiplicative identity, 1
vector space property 8: distribution of scalars over vectors
vector space property 9: distribution of vectors over scalars
vector space property 10: associativity of scalar multiplication](https://content.bartleby.com/qna-images/question/ad61a16a-ccb3-4100-87e8-33e1dead9976/bda4cdbb-a4ba-4b52-8697-5d5efd397c95/lc7mfxa_processed.png)
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