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Math Help - Vector Space Question

  1. #1
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    Vector Space Question

    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.
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  2. #2
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    Mar 2009
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    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...
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