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Math Help - FInd a basis

  1. #1
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    FInd a basis

    I need to find a basis for the following:
    {x belongs to R5, x1=x2, x3=x4) in R5
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  2. #2
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    Quote Originally Posted by chadlyter View Post
    I need to find a basis for the following:
    {x belongs to R5, x1=x2, x3=x4) in R5
    Let,
    x1=x2=s
    x3=x4=t
    x5=r

    Any element in this subspace is,

    [x1 x2 x3 x4 x5] = [s s t t xr]
    Write as,
    [s s 0 0 0] + [0 0 t t 0] + [0 0 0 0 r]
    Factor,
    s[1 1 0 0 0] + t[0 0 1 1 0] + r[0 0 0 0 1]
    We can see that,

    {[1 1 0 0 0], [0 0 1 1 0], [0 0 0 0 1]}
    Is the basis for this subspace.
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