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Math Help - Matrix associated to a linear map

  1. #1
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    Matrix associated to a linear map

    R^3 = L(direct sum)W,with dim(L)=1.Suppose T:R^3--->R^3 is a linear map.T(L)subset of L and T(W)subset of W.
    Find a basis B of R^3 such that m(T;B) is a 3*3 matrix with entries...a(11) nonzero number, a(21) zero, a(31) zero, a(12) zero, a(22) nonzero number, a(32) nonzero number, a(13) zero, a(23) nonzero number, a(33) nonzero number..
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  2. #2
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    Quote Originally Posted by math.dj View Post
    R^3 = L(direct sum)W,with dim(L)=1.Suppose T:R^3--->R^3 is a linear map.T(L)subset of L and T(W)subset of W.
    Find a basis B of R^3 such that m(T;B) is a 3*3 matrix with entries...a(11) nonzero number, a(21) zero, a(31) zero, a(12) zero, a(22) nonzero number, a(32) nonzero number, a(13) zero, a(23) nonzero number, a(33) nonzero number..
    Choose non-zero vectors v_1, v_2, v_3 so that v_1 is in L (and since L has dimension 1, { v_1} is a basis for L) and { v_2, v_3} is a basis for W. You can do that because L directsum W= R^3. Applying T to v_1 you get Tv_1= av_1+ 0v_2+ 0v_3 because T maps L to itself. Applying T to either v_2 or v_3 gives 0v_1+ bv_2+ cv_3 because T maps W to itself.
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  3. #3
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    W is not mentioned which plane it is..so can i take any two vectors..(like (1,0,-1/2),(0,1,-3/4) )..n what is the use of the condition T(L) subset of L and T(W) subset of W..is it used to find the linear map as the map is not mentioned..n what happens when T(L) subset of W and T(W) subset of L..
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    Quote Originally Posted by math.dj View Post
    W is not mentioned which plane it is..so can i take any two vectors..(like (1,0,-1/2),(0,1,-3/4) )..n what is the use of the condition T(L) subset of L and T(W) subset of W..is it used to find the linear map as the map is not mentioned..n what happens when T(L) subset of W and T(W) subset of L..
    If you really have no idea what the question is asking (and it appears from this that you don't) the best thing you can do is go to your teacher and ask for more explanation.
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  5. #5
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    Thx for the advice..
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