Question

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

Answer 1

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.