Describe the zero vector (the additive identity) of the vector space. R^4

emancipezN 2021-10-31 Answered
Describe the zero vector (the additive identity) of the vector space.
R4
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Expert Answer

Theodore Schwartz
Answered 2021-11-01 Author has 99 answers
Every vector in R4 can be represented as
υ=(υ1,υ2,υ3,υ4)
We have to find the additive identify vector - the vector that has following property:
υ+x=x+υ=υ
In coordinate notation:
(υ1,υ2,υ3,υ4)+(x1,x2,x3,x4)=(υ1+x1,υ2+x2,υ3+x3,υ4+x4)=(υ1,υ2,υ3,υ4)
υ1+x1=υ1
υ2+x2=υ2
υ3+x3=υ3
υ4+x4=υ4
From properties of addition in R, we know that x1=x2=x3=x4=0
So, additive identity vector is x=(0,0,0,0)
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