Diagonalize the matrix A = [1,1;-2,4] using a similarity transformation. Give the transformation matrices such that (C^−1)AC = D, where D is a diagonal matrix. (D, C) = ?

Answer 1

The eigenvectors of A are (1,2) and (1,1)

So, C = [1,1;2,1] and C^-1=[-1,1;2,-1]

C^-1 A C = [3,0;0,2]

See

http://www.wolframalpha.com/input/?i=%28inverse+{{1,1},{2,1}}%29*{{1,1},{-2,4}}*{{1,1},{2,1}}