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Math Help - T saved subspaces question

  1. #1
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    T saved subspaces question

    sorry wrong forum
    Last edited by transgalactic; October 15th 2011 at 04:09 PM.
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  2. #2
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    Re: T saved subspaces question

    clearly the subspace generated by the basis {(1,0,0)} is T-invariant, since that is E2.

    also the subspace generated by {(0,0,1)} is T-invariant, since that is E3.

    therefore the subspace generated by the basis {(1,0,0),(0,0,1)} is also T-invariant. a vector in this subspace is of the form (a,0,b),

    and T(a,0,b) = (2a,0,3b) = 2a(1,0,0) + 3b(0,0,1).

    two more obvious T-invariant subspaces are R^3 itself, and the 0-subspace.

    a less obvious T-invariant subspace is the subspace generated by the basis {(1,0,0),(0,1,0)}. any vector in this subspace is of the form (a,b,0),

    and T(a,b,0) = (2a+b,2b,0) = (2a+b)(1,0,0) + 2b(0,1,0).

    so that's 6, you should be covered.
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  3. #3
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    Re: T saved subspaces question

    its not the correct forum i have replied in the lenear algebra forum on this subject
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