1. Suppose
$A \left[\matrix{4 \cr 5}\right] = \left[\matrix{4 \cr 5}\right]$,
$A \left[\matrix{3 \cr 5}\right] = \left[\matrix{9 \cr 15}\right]$,
$A \left[\matrix{4 \cr 5}\right] = \left[\matrix{4 \cr 5}\right]$,
$A \left[\matrix{2 \cr 1}\right] = \left[\matrix{-4 \cr -2}\right]$
State the 2 eigenvalues of $A$:
State 5 eigenvectors of $A$:
2. The radius of convergence of the power series for $f(x) = {x \over (x^2 + 1)(x + 2)}$ about the point $x_0 = {1 \over 4}$ is $\geq \sqrt{({1 \over 4})^2 + (\pm 1)^2} = {\sqrt{17} \over 4}$
A) True
B) False
3.) ${x \over (x^2 + 1)(x + 2)}$ $= \Sigma_{n=0}^\infty a_n(x - {1 \over 4})^n$ where $a_n = {f^{(n)}( {1 \over 4}) \over n!}$ for all values of $x \in ({1 - \sqrt{17} \over 4}, {1 + \sqrt{17} \over 4})$.
A) True
B) False