Determine la ecuación característica, los valores caracteristicos y los vectores característicos asociados a la matriz \( 4 \times 4 \) [video guía; https://youtu,be/iJu78zgRpjo] \[ \left[\begin{array}{cccc}1 & 0 & -1 & 1 \\ 0 & 1 & 0 & 1 \\ -2 & 0 & 2 & -2 \\ 0 & 2 & 0 & 2\end{array}\right] \]

2imalify \( \frac{x^{2}-y^{2}}{x^{2} x y} \) \( \frac{y+2 x-3 y}{3 x-2 y}=4 \), evaluate \( 2 x y \) If \( z=\sqrt{x^{2}-y^{2}} \), express \( x \) interm 9 \( y \) and 2

Question 8 ( 3 marks) What is the equation of the line that passes through the points \( (1,6) \) and \( (3,2) \) ? \( y=\square x+\square \)

ii) \( \frac{4 x^{2}+3 x+7}{x+1} \)

2.3 Express \( \frac{1}{\sqrt{2}+1} \) in its simpl

5. Separen en términos y resuelvan. a. \( \left(-\frac{4}{3}+\frac{1}{6}\right)-\left(-\frac{3}{2}\right)^{-2}+\sqrt[3]{\left(\frac{3}{4}+\frac{1}{8}\right)-} \) b. \( \left(\frac{3}{2}-\frac{1}{2}\right)^{2}+\sqrt[3]{-\frac{1}{64}}-0.5= \) c. \( \sqrt[3]{1-\frac{7}{8}}-\left(-\frac{2}{5}+\frac{1}{10}\right)^{-4}+0.3- \) d. \( -\left(\frac{8}{5}-\frac{6}{15}\right)-\sqrt[3]{1-\frac{31}{32}}+\left(\frac{7}{5}\right)^{2}= \)