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Math Help - Dimensions and Subspaces Help

  1. #1
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    Dimensions and Subspaces Help

    Determine the dimensions of the following subspaces of R^2 and R^3?

    1. R^3= span{(-2, -12, 10), (-1, 3, -4), (2, 3, -1)}
    2. R^2= span{(4, 2), (2, 0), (5, 0), (9, 1), (2, 3)}
    3. R^2= span{(7, 2), (6, 5)}
    4. R^2= span{(0, 0)}
    5. R^3= span{(20, 4, 8), (1, 4, 2), (10, 2, 4), (4, 3, 4)}
    6. R^2= span{(5, 7), (6, 7, 8), (4, 8, 2)}


    How would I go about doing this problem?
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  2. #2
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    Quote Originally Posted by My Little Pony View Post
    1. R^3= span{(-2, -12, 10), (-1, 3, -4), (2, 3, -1)}
    ...
    How would I go about doing this problem?
    Vectors that span a subspace contain all the information you need to construct a basic for the subspace. Do you know how to calculate a basis of C(A)? If so, you should know that the columns of A span C(A). The columns of A can also a basis of C(A), but <==> A is invertible (all columns are Linearly Independent).
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  3. #3
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    In other words, construct a matrix having those vectors as columns and row-reduce. The dimension of their span is the number of non-zero rows you get.
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