Polynomial equations and recurrence relations are fundamental concepts in mathematics that have wide-ranging applications in various fields, including computer science, physics, and engineering.

Topics covered: Matrix methods in portfolio analysis. Linear independence. Rank of a matrix. Eigenvalues and eigenvectors. Diagonalisation. Linear systems of recurrence equations. Markov process.

A sequence is defined by the recurrence relation \({U_n} = m{U_{n - 1}} + c\) Find the values of \(m\) and \(c\) if \({U_1} = - 3\), \({U_2} = 7\) and \({U_3} = 10 ...