I'm supposed to find the matrix P here. I've found the characteristic polynomial p(lamda) = -x - x^2 + x^3 + x^4 (just writing x instead of lamda). And I found the roots:
But I can't make sense of what the book does next to find P... Any help would be very appreciated! =)
They don't tell you any more information? When you say "find the matrix P", do you mean find the 4x4 matrix with all of its values? Because I think that is impossible just given the characteristic polynomial. Multiple 4x4 matrices can yield that same polynomial. Also there are two -1 roots, just fyi...
This is a fourth degree polynomial. There needs to be four solutions. What was the matrix that gave you those lambda?
To obtain your eigenvectors, you need to plug in each lambda and then rref the matrix. Then do that for the other eigenvalues until you have 4 eigenvectors. If you don't obtain 4 eigenvectors, this matrix isn't diagonalizable.
Please write the entire problem! I suspect the respondents are correct, that you are given a matrix, A, and are asked to find the matrix P such that where D is a diagonal matrix having the eignvalues of A on its diagonal. But what P is depends strongly on what A is- and different matrices can have the same characteristic polynomial.
dwsmith- he did give all roots. -1 is a double root.
I understand but it should have been noted.
Originally Posted by HallsofIvy