fast help in algebra; eigenvectors written as linear comb.
- Thread starter jul4ka
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What have you tried so far?
Have you written (1,2) as a linear combination of the eigenvectors?
If so, remember that if x1 and x2 are the eigenvectors, with eigenvalues lam1 and lam2, then Axi = lami xi, so also A(a x1 + b x2) = a lam1 x1 + b lam2 x2. Then you can find A^n (a x1 + b x2) by repeatedly multiplying by A.
Let us know if you're still stuck.
Have you written (1,2) as a linear combination of the eigenvectors?
If so, remember that if x1 and x2 are the eigenvectors, with eigenvalues lam1 and lam2, then Axi = lami xi, so also A(a x1 + b x2) = a lam1 x1 + b lam2 x2. Then you can find A^n (a x1 + b x2) by repeatedly multiplying by A.
Let us know if you're still stuck.
thank you, i also tried this, just wasnt sure if i do it right 
from a i had eigenvalues (3;-1)
i did following
x0=x*a+y*b
i found a and b a=-0.5 b=1.5
then i insert xt= (1,1)*(1.5*3^t)+(1,-1)*0.5*(-1)^t+1
into formula i inserted eigenvalues from a solution
thank you a lot for help
from a i had eigenvalues (3;-1)
i did following
x0=x*a+y*b
i found a and b a=-0.5 b=1.5
then i insert xt= (1,1)*(1.5*3^t)+(1,-1)*0.5*(-1)^t+1
into formula i inserted eigenvalues from a solution
thank you a lot for help