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Math Help - Find a basis

  1. #1
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    Find a basis

    I don't know why this one is giving me such a hard time but it is:

    Find a basis for the set of vectors in R^3 in the plane x + 2y + z = 0



    Thank you!
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by baxyjr View Post
    I don't know why this one is giving me such a hard time but it is:

    Find a basis for the set of vectors in R^3 in the plane x + 2y + z = 0
    Any two vectors of the plane which don't share the same direction will give you a basis of this plane. To find two such vectors one can pick up three points A, B and C on the plane and check that \vec{AB} \nparallel \vec{BC}.
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  3. #3
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    Quote Originally Posted by flyingsquirrel View Post
    Hello

    Any two vectors of the plane which don't share the same direction will give you a basis of this plane. To find two such vectors one can pick up three points A, B and C on the plane and check that \vec{AB} \nparallel \vec{BC}.
    Thank you!

    Ok, I think I get it.

    So you're saying that as long as I pick two vectors in R3 that are linearly independent and satisfy the equation, that I am good?

    Thank god for this site! Especially when you are taking a class that normally covers 4 months in four weeks!

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  4. #4
    MHF Contributor Reckoner's Avatar
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    Quote Originally Posted by baxyjr View Post
    Thank you!

    Ok, I think I get it.

    So you're saying that as long as I pick two vectors in R3 that are linearly independent and satisfy the equation, that I am good?
    Yes. The plane will be a vector space of dimension 2, so any two linearly independent vectors in it will form a basis.
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