Given three eigenvectors and three eigenvalues, how would you go about finding BOTH non-symmetric matrix A and symmetric matrix B?

EDIT 7/27: Sorry for not being specific enough~ In the problem I am given three linearly independent 4x1 eigenvectors and their respective eigenvectors.

Then, I am asked to find a non-symmetric matrix A and a symmetric matrix B. Matrices A and B share these eigenvectors and eigenvalues.

Given three eigenvectors and three eigenvalues, how would you go about finding BOTH non-symmetric matrix A and symmetric matrix B?

EDIT 7/27: Sorry for not being specific enough~ In the problem I am given three linearly independent 4x1 eigenvectors u1, u2, and u3 and their respective eigenvectors. I found out that every vector pairing is orthogonal EXCEPT between u1 and u2 because their dot product is non-zero.

Then, I am asked to find a non-symmetric matrix A and a symmetric matrix B. Matrices A and B share these eigenvectors and eigenvalues.

Given three eigenvectors and three eigenvalues, how would you go about finding BOTH non-symmetric matrix A and symmetric matrix B?

Given three eigenvectors and three eigenvalues, how would you go about finding BOTH non-symmetric matrix A and symmetric matrix B?

EDIT 7/27: Sorry for not being specific enough~ In the problem I am given three linearly independent 4x1 eigenvectors and their respective eigenvectors.

Then, I am asked to find a non-symmetric matrix A and a symmetric matrix B. Matrices A and B share these eigenvectors and eigenvalues.