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Math Help - find the general solution...

  1. #1
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    find the general solution...

    ok here is my problem...





    ok so when i started this problem i found that the values of lambda were 1/2 and
    -1/2

    so my first solution is...

    this solution was for when lambda was 1/2.

    my problem comes when lambda is -1/2...

    i basically have 2 equations k1 +(0)k2 = 0 and k1+(0)k2 = 0? so am i to assume that k1 and k2 are 0?

    any thoughts would be appreciated.
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  2. #2
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    Quote Originally Posted by slapmaxwell1 View Post
    ok here is my problem...





    ok so when i started this problem i found that the values of lambda were 1/2 and
    -1/2

    so my first solution is...

    this solution was for when lambda was 1/2.

    my problem comes when lambda is -1/2...

    i basically have 2 equations k1 +(0)k2 = 0 and k1+(0)k2 = 0? so am i to assume that k1 and k2 are 0?

    any thoughts would be appreciated.
    No that tells you that

    k_1=0

    but

    k_2

    is free so you get the eigenvector

    \begin{pmatrix} 0 \\ 1\end{pmatrix}
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