Ok, let's say we want to prove that its commutative.
Can I do the following?
(a1,a2)+(b1,b2)=(a1+b1,a2+3b2)=(b1+a1,3b2+a2)=(b1, b2)+(a1,a2)
Just any indication of how to do this problem properly will be very helpful...
V={ (a1,a2) : a1,a2 elements in R}
For (a1,a2),(b1,b2) elements of V & c element of R
Define:
(a1,a2)+(b1,b2)=(a1+b1,a2+3b2)
c(a1,a2)=(ca1,ca2)
Is V a vector space over R with these operations?(justify)
I would really appreciate it if someone could give me an explanation about how im supposed to approach a problem like this.
Thanks in advance.