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Math Help - Basis

  1. #1
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    Basis

    Find a basis for R^4 includes the vectors: (1,0,1,0) and (0,1,-1,0)
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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    Find a basis for R^4 includes the vectors: (1,0,1,0) and (0,1,-1,0)
    Does (1,0,0,0)\;\&\;(0,0,0,1) do it?
    How would you prove or disprove it?
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  3. #3
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    Quote Originally Posted by Plato View Post
    Does (1,0,0,0)\;\&\;(0,0,0,1) do it?
    How would you prove or disprove it?

    I did not understand
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  4. #4
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    Quote Originally Posted by Apprentice123 View Post
    I did not understand
    What is there to understand?
    Do you know what a basis is?
    Do you know what properties are required?
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  5. #5
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    Remember a basis is a linear independent spanning set. A Basis of \mathbb{R}^4 is going to consist of 4 linear independent vectors. So all you do is take the 2 vectors they gave you and find 2 other linear independent vectors. As Plato suggested just take 2 vectors from the standard basis and see if they are linear independent.
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