Question

Consider the set 

V=R

. Define the addition operation on 

V

 as follows: for 

u,v∈V

 , define 

u+v:=u−v


  where 

u−v

 is the usual subtraction of 

v from u

. Define scalar multiplication as follows: for 

a∈R ,define 

a.u:=a^2u

. Determine the following (Problem1 to Problem 4).



1).

Is V

 closed under vector addition?

Yes

 

No

2).

Is V

 closed under scalar multiplication?

Yes

 

No

3).

Which of the properties in the definition of a vector space that were given in the lecture, are satisfied by 

V

 with these operations?

Property I (Commutativity)

 

Property II (Associativity)

 

Property V (Existence of multiplicative identity)

 

Property VII (Distributivity)

 

Property VIII (Multiplication is linear)

4).

Is 

V

 a vector space with these operations?

Yes

 

No

​

Answer 1

Answer:

yes

v

Step-by-step explanation:

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