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Math Help - orthogonality

  1. #1
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    orthogonality

    Consider vectors v1, v2, v3 in R^4; we are told that (vi dot vj) is the entry aij of matrix A. A =

    [3 5 11]
    [5 9 20]
    [11 20 49].

    Find length of (v1 + v2). For this I got 2(sqrt(3)). Can someone check this?

    Also, find projV(v3), where V = span(v1, v2). Express your answer as a linear combination of v1 and v2.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Can you post your work so we can check it?
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  3. #3
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    ||v1 + v2|| = sqrt((v1 dot v1) + (v2 dot v2)) = sqrt((a11) + (a22)) = sqrt(3 + 9) = sqrt(12) = 2sqrt(3)
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  4. #4
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    and I'm not sure where to do on the projV(v3) question
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