Find a 3x3 matrix A that has eigenvalues = 0, 1, -1 with corresponding eigenvectors (0,1,-1), (1,-1,1), (0,1,1)

Question

Find a 3x3 matrix A that has eigenvalues  = 0, 1, -1 with corresponding eigenvectors (0,1,-1), (1,-1,1), (0,1,1)

anonymous · Answer

Since you are given the eigenvectors and eigenvalues, you have enough information to form the diagonalized form of your matrix.  Let A be the matrix you want.  Then:$$A=SDS^{-1}$$ where S is the matrix formed by your eigenvectors, S^-1 is the inverse of that matrix, and D is a diagonal matrix with the eigenvalues on the diagonal.  

Basically, you have the information to find S, S^-1 and D, and once you find those multiply everything out to get the answer.