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#7 prime factor of the form p). Make a conjecture about what happens to the fraction of square free numbers as N goes to infinity. #8. The Perron-Frobenius Theorem is a very useful theorem that asserts that a real square matrix with positive entries has particular constraints on its spectrum (eigenvalues and vectors). The theorem is often used in dynamical systems and probability. One of the consequences of the theorem is that for particular matrices (called irreducible and non-negative), the following sequence has a certain behavior kl. " Where is the largest eigenvalue of "A. Using the matrix 2 3 A=1456 7 89 (which is ireducible and nonnegative), conjecture about what happens to the above sequence. #7 prime factor of the form p). Make a conjecture about what happens to the fraction of square free numbers as N goes to infinity. #8. The Perron-Frobenius Theorem is a very useful theorem that asserts that a real square matrix with positive entries has particular constraints on its spectrum (eigenvalues and vectors). The theorem is often used in dynamical systems and probability. One of the consequences of the theorem is that for particular matrices (called irreducible and non-negative), the following sequence has a certain behavior kl. " Where is the largest eigenvalue of "A. Using the matrix 2 3 A=1456 7 89 (which is ireducible and nonnegative), conjecture about what happens to the above sequence