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    I know how to find the eigenvalues (lambda) and then I can put them back into that A - Lambda*I matrix, and then I know you have to multiply this by a general vector 'v'. Lets assume for now that it's a 2 x 2 matrix, so v= (x,y). And I also know that you let all this equal to 0. You then multiply out the matrix and you get 2 equations that equal 0. What do you do from here?
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    Solve those equations and express one component in terms of the other. (There isn't a unique solution. If you have a unique solution then you have made an error.)
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    (Original post by Zhen Lin)
    Solve those equations and express one component in terms of the other. (There isn't a unique solution. If you have a unique solution then you have made an error.)
    Can you pick 4 random numbers so we can create an example because the bit I have trouble with is that whole expressing one in terms of the other and how to write that down. If you pick 4 numbers then you're not giving me a solution to my homework and mods can't do anything about that right
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    (Original post by claret_n_blue)
    Can you pick 4 random numbers so we can create an example because the bit I have trouble with is that whole expressing one in terms of the other and how to write that down. If you pick 4 numbers then you're not giving me a solution to my homework and mods can't do anything about that right
    Take a 2x2 matrix:

    \begin{pmatrix}  5 & 3 \\  2 & 4\end{pmatrix}

    The eigenvalues are 7 and 2.

    Take the eigenvalue 7 and put it into the equation and you get:

    \begin{pmatrix} -2 & 3 \\2 & -3 \end {pmatrix}\begin{pmatrix} x \\y \end {pmatrix} = \begin{pmatrix} 0 \\0 \end {pmatrix}

    The equations are:

    -2x + 3y = 0
    2x - 3y = 0

    These are both 3y = 2x

    Let x=k

    y= (2/3)k

    The eigenvector is therefore

    k\begin{pmatrix} 1 \\\frac{2}{3} \end {pmatrix}

    Which can be written as:

    k\begin{pmatrix} 3 \\\ 2 \end {pmatrix}

    A similar thing can be done with the eigenvalue 2.
 
 
 
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