Are the following statements true or false for a square matrix A? 1. If an n x n matrix A is diagonalizable, then A has n distinct eigenvalues. 2. Finding an eigenvector of A might be difficult, but checking whether a given vector is in fact an eigenvector is 3. The eigenvalues of a matrix are the entries on its main diagonal. 4. If u and v are linearly independent eigenvectors, then they correspond to distinct eigenvalues. 5. A matrix A is singular if and only if 0 is an eigenvalue of A.

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