Eigenvalues and vectors - finding original matrix

[Caeder]

How do I determine what the original matrix was that yielded these two eigenvalues with the corresponding eigenvectors:

$$\lambda_1 = -3$$ Eigenvector: [0,1]

$$\lambda_2 = 2$$ Eigenvector: [1,0]

I've played around with det(A-lambda I) but can't find the matrix! I even just did some trial and error matrices in Maple trying to figure it out. If anyone can find me the matrix I'd be very impressed.

 

[rock.freak667]

Well if you have the eigenvectors of a matrix A then A can be represented as:
A=PDP$^{-1}$
where D is a diagonal matrix with the diagonal elements as $\lambda_1 \ and \ \lambda_2$

and P is the eigenvectors of the eigenvalues...

so from your problem:

D would be the matrix:
[-3 0]
[0 2]

and the first column for P would be the eigenvector for -3 and the 2nd column would be the eigenvector for 2...so you now have P..find P$^{-1}$ and multiply out

 

[Office_Shredder]

What does the matrix
a₁₁ a₁₂
a₂₁ a₂₂

map (1,0) and (0,1) to?