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Math Help - Am i correct?

  1. #1
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    Am i correct?

    I have to find a basis for the vector space spanned by these 3 column vectors:
    [1;-1;2] [2;-3;2] and [1;-3;2]

    I have written the vectors as rows of an array and solved as far as possible:
    pivot rows are in bold and -1--> means add to -1*pivot row

    1 -1 2
    |
    2 -3 2| -2 -->
    1 -3 2| -1 -->
    -1 -2|
    -2 -6| -2-->
    0 0 -2

    does this mean that one possible basis is: {[1;-2;2],[0;-1;-2],[0;0;-2]}?


    Also does this mean that the dimension for the subspace is 3?
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  2. #2
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    Quote Originally Posted by deragon999 View Post
    I have to find a basis for the vector space spanned by these 3 column vectors:
    [1;-1;2] [2;-3;2] and [1;-3;2]

    I have written the vectors as rows of an array and solved as far as possible:
    pivot rows are in bold and -1--> means add to -1*pivot row

    1 -1 2
    |
    2 -3 2| -2 -->
    1 -3 2| -1 -->
    -1 -2|
    -2 -6| -2-->
    0 0 -2

    does this mean that one possible basis is: {[1;-2;2],[0;-1;-2],[0;0;-2]}?


    Also does this mean that the dimension for the subspace is 3?
    It's enough to prove that the three vectors are independent. Then the three vectors themselves form a basis for the vector space.

    Dimension of vector space = size of basis therefore dimension of the vector space is equal to 3.
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  3. #3
    Junior Member
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    Thanks

    Ok i fully understand that..but just because i spent the time on it..is my basis also true..or does that way only work if the vectors are Dependant?
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