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thdrbird
Group Title
Let A = [3,2,6
0,1,6
0,0,3]
Find an invertible matrix P and a diagonal matrix D such that D = P^{1}AP.
find P and D
I worked out the polynomial 7x^37x^215x9 to give x= 1,3,3
My answer for P= [1,0,0
1,3,3
0,1,1]
and D= 1,0,0
0,3,0
0,0,3
something's wrong!
 one year ago
 one year ago
thdrbird Group Title
Let A = [3,2,6 0,1,6 0,0,3] Find an invertible matrix P and a diagonal matrix D such that D = P^{1}AP. find P and D I worked out the polynomial 7x^37x^215x9 to give x= 1,3,3 My answer for P= [1,0,0 1,3,3 0,1,1] and D= 1,0,0 0,3,0 0,0,3 something's wrong!
 one year ago
 one year ago

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electrokid Group TitleBest ResponseYou've already chosen the best response.2
what type of decomposition are you doing here ?
 one year ago

Hoa Group TitleBest ResponseYou've already chosen the best response.1
I think you get something wrong at P, since eigenvalue 3 has 2 dimensions and they are not yours! recheck
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
you should get D=dia(3,1,3)
 one year ago

Hoa Group TitleBest ResponseYou've already chosen the best response.1
yes, surely, because they are eigenvalues of A, what I need is checking the order this guy arrange in P to have corresponding of numbers, like (3,1,3) or (1,3,3)
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
ok I will try!
 one year ago

Hoa Group TitleBest ResponseYou've already chosen the best response.1
We cannot guess, right, kid? if we mess the order up, although we know it is the Diagonal matrix of A but the P is in different order of eigenvectors, We will be crazy when checking what wrong is, I had that experience. It made me crazy
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
tr(A)=313=7 A11+A22+A33=3+9+3=15 A=3(3)=9 so, the characteristic polynomial would be\[\Delta(t)=t^3+7t^2+15t+9\]
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
well, as long as the eigen vector columns are arranged in proper order, you should be good.
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
still no luck...
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
eigen vectors=? for t=1: \[2x+2y+6z=0\\6z=0\\3z=0\implies v_1=(1,1,0)^T\]
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
and v2 and v3 I put at (0,3,1)
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
for t= 3: \[ 2y+6z=0\\ 2y+6z=0\\ v_{2,3}=(\alpha,3\beta,\beta)^T \]
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
@thdrbird you cannot have them two identical
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
you can use v2 when a=0,b=1 v3 when a=1,b=1
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.2
or v3 when a=1,b=0 ANY combination of alpha and beta that do not give the same vectors..
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
can you give me an example?
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
I forgot to set alpha!
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
thanks @electrokid, great help!
 one year ago

thdrbird Group TitleBest ResponseYou've already chosen the best response.0
@Hoa as well! Thanks!
 one year ago

Hoa Group TitleBest ResponseYou've already chosen the best response.1
I did nothing guy!!!
 one year ago
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