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Math Help - 2 questions need help

  1. #1
    Junior Member
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    2 questions need help

    1) IN C[ 0 , 1 ], find the projection of t + 1 onto t^2

    2) Let W be the subspace of R^3 spanned by 1 and 0
    0 1
    1 0

    A) find the distance between 3 and the nearest vector in W
    2
    1

    B) write 3 as w + u, were w is in W and u is in W^(upside down T)
    2
    1


    didnt know what the word for the symbol was, but it looks like an upside down T
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  2. #2
    Junior Member
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    vectors got messed up

    vectors got messed up when submited

    2) vectors:

    1 0
    0 1
    1 0

    A) vectors:

    3
    2
    1

    B) vectors:

    3
    2
    1
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by luckyc1423
    1) IN C[ 0 , 1 ], find the projection of t + 1 onto t^2
    Usually I would take the projection of \bold u onto \bold v to be \frac{\langle \bold u,\bold v\rangle}{\|\bold v\|}\hat{\bold v}=\frac{\langle \bold u,\bold v\rangle}{\|\bold v\|^2} \bold v .

    On C[0,1] we would normally use:

    <br />
\langle \bold f, \bold g \rangle =\int_0^1 \overline{\bold{f}(x)}\bold{g}(x) dx<br />

    and:

    <br />
\|\bold{f}\|=\langle \bold{f},\bold{f}\rangle^{1/2}<br />

    RonL
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