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Math Help - Constructing bases (basis)

  1. #1
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    Constructing bases (basis)

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    I know how to construct U1, U2 and U1 intersect U2, but how do i construct U1 + U2?

    U1 is the matrix of L1 and I just row reduced it etc.
    U2 is the matrix of L2 and i just row reduced it etc.
    U1 intersect U2 is the matrices added together (making it 4 rows), and row reducing it.

    But how do i do U1+U2? Thanks.
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  2. #2
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    one way is to take the union of the basis for U1, with the basis of U2, and then to remove any linearly dependent elements.

    dim(U1+U2) = dim(U1) + dim(U2) - dim(U1∩U2), so you already know how many elements you should wind up with.
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  3. #3
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    Thanks!
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