Please help me with this Linear Algebra question which invol

Please help me with this Linear Algebra question which involves using axioms to define addition and scalar multiplication. Also, find what axiom fails the vector space? Please be DETAILED. If you cannot be detailed, don\'t answer the question. I will rate the answer based on the explanation and work shown. I\'m having trouble with this material and need to understand it.

Thank you.

Solution

lets take

(a1, b1)+(c1,d1)

According to the definition

(a1+c1, b1.d1)

and lets take it vice versa...

(a2+c2, b2.d2)

(a2+b2, c2+d2)

Lets take some example

(1+2,3+6)

(1+3, 2.6)

(4,12)

And for multiplication case,

k(a,b)

(ka,b)

in this case,

k(a1,b1)

(ka1,b1).