Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (b)/Statement

Let $\lambda _{1}$ and $\lambda _{2}$ denote the two eigenvalues of the matrix A. Compute $\lambda _{1}$ and $\lambda _{2}$ and two associated eigenvectors ${\bf {x}}_{1}$ and ${\bf {x}}_{2}$. Find some constants $a$ and $b$ such that:

$${\begin{bmatrix}d_{n}\\s_{n}\end{bmatrix}}=a\lambda _{1}^{n}{\bf {x}}_{1}+b\lambda _{2}^{n}{\bf {x}}_{2}.$$