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Math Help - Bases for R2

  1. #1
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    Bases for R2

    Course: Linear Algebra

    So I have the set \left\{(0,0) , (1,3)\right\} which I will call S.

    I'll have the system:

    c_2 = x_1
    3c_2 = x_2

    Which gives me c_2 = x_1 = \frac{1}{3}x_2

    Can this mean that span(S) = R2?
    Is the zero vector redundant?
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  2. #2
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    Re: Bases for R2

    Hey MadSoulz.

    Yes the zero vector is not necessary and you should know that the zero vector is linearly dependent to any other vector since 0*any_vector = 0 vector no matter what vector you use.
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  3. #3
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    Re: Bases for R2

    Thanks chiro.
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