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Find orthogonolised base

  1. Feb 18, 2009 #1
    i got these vectors R4:
    v1=(1,1,0,1)
    v2=(0,-4,2,0)
    v3=(0,0,-18,0)
    u1=(1,1,0,1)
    u2=(-1,0,1,0)


    in the row reduction process v1 v2 v3 u1 are left independent
    i need to find the orthogonal base of u+v?

    in the solution i was told that because v1 v2 v3 u1 are independent

    then the orthogonal base of u+v the standard base of is
    (1,0,0,0)
    (0,1,0,0)
    (0,0,1,0)
    (0,0,0,1)

    but why take the standart base
    the vectors v1 v2 v3 u1 are independent they can act as a base
    ??
     
  2. jcsd
  3. Feb 18, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You have left some things out. Are we to assume that v is spanned by v1, v2, and v3? And that u is spanned by u1 and u2?

    Yes, v1, v2, v3, u1 are independent and so are a basis for u+v. But they are not orthogonal. Since there are four of them, they span all of R4. You know that the standard basis for R4 is orthonormal so it satisfies the conditions of the problem: Find an othogonal basis for u+ v.
     
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