finding the eigen value
\[\lambda(\lambda-4)(\lambda-3)+7-9(\lambda-4)-(\lambda-3)=0\]
@lawls
uhhh
guess
\[\lambda = .... ,. ..??\]
what was ur matrix
i wanna see how u got that 7 there
check 2 and -2
are you trying to diogonalize ?
Why not distribute everything and make it of the form \[\LARGE a \lambda ^3+b \lambda^2+c \lambda + d=0\]
You can then graph it on your calculator and use that to essentially "guess" the factors.
there seems to be something wrong.. usually the matrix is cooked up such that the characteristic eq'n is easily solvable..
http://www.wolframalpha.com/input/?i=solve+x%28x-4%29%28x-3%29%2B7-9%28x-4%29-%28x-3%29%3D0
\[\lambda( \lambda^2-7*\lambda+12)+7-9\lambda+36-\lambda+3\]
\[\lambda^3-7*\lambda^2+12*\lambda+7-10\lambda+46=0\]
\[\lambda^3-7\lambda^2+2\lambda+53=0\]
\[\lambda=-2.28, 4.64 , 4.64\]
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