1. Given the following matrix, (a) find the eigenvalues and eigenvectors of A. (b) What do your findings tell you about the rank of A? 2. Given the following eigenvalues with their corresponding...

1. Given the following matrix,

(a) find the eigenvalues and eigenvectors of A.

(b) What do your findings tell you about the rank of A?

2. Given the following eigenvalues with their corresponding eigenvectors, and knowing that the original matrix was square and symmetric, reconstruct the original matrix.