SOLUTION: Let A= [−47 −90 ; 27 52]. Find S, D, and S^−1 such that A=SDS^−1

We diagnalize the matrix:



We find the eigenvalues











 λ-7=0;  λ+2=0   
   λ=7;   λ=-2

by writing A as 



where D is the diagonal matrix with the two eigenvalues on the 
main diagonal:



and the matrix S is 



where the V's are the two column eigenvectors for the two eigenvalues

We find V1 which is the eigengvector for the eigenvalue λ=7.

We find solutions for








Divide thru by -18



We can take x1=1 and x1=1

So 



Now we do the same for the other eigenvalue

---

We find solutions for








Divide thru by -45



We can take x1=1 and x2=1

So 



So



And since the determinant of S is 1, to find S-1 we only
need to swap the elements on the the main diagonal and change the
signs of the other two elements"



Then 





Edwin