Un alumno tiene que elegir 7 de las 10 preguntas de un examen. ¿De cuántas maneras puede elegirlas? ¿Y si las 4 primeras son obligatorias?

3. Sean \( v_{1}=\left[\begin{array}{l}2 \\ 1\end{array}\right], v_{2}=\left[\begin{array}{c}-3 \\ 1\end{array}\right] \) y \( v_{3}=\left[\begin{array}{c}1 \\ -2\end{array}\right] \). Justifique lo siguiente: (a) ¿Los vectores \( v_{1} \cdot v_{2} \) y \( v_{3} \) son lineamentes independientes?. (b) ¿El conjunto \( \left\{v_{1}, v_{3}\right\} \) es una base para \( \mathbb{R}^{2} \) ?. (c) \( ¿ \) El generado por \( \left\{v_{1}, v_{2}\right\} \) es igual al generdo por \( \left\{v_{1}, v_{3}\right\} \) ?.

Ex 4: Give the opposite a) A merciful king

3.20. Para \( n \in \mathbb{Z}^{+} \)se define \( f(n) \) como el número de enteros positivos \( <n \) que son primos relativos con \( n \), por ejemplo \[ \begin{aligned} f(1)=1, \\ f(2)=1, \\ f(3)=2, \\ f(4)=2\end{aligned} \] 3.20.1. Calcular \( f(10), f(13), f(18), f(24) \) \( \begin{array}{l}\text { 3.20.2. Para } n=12,18,19,25 \text { calcule } \\ \text { 3.20.3. Infiera una fórmula para } \\ \qquad\end{array} \)

Match the type of noun below to its correct name. Abstract Noun Cat Team

Which of the following statements islare TRUE of the major schools of economic thought? i. Keynesians believe in the use of macroeconomic tools to stabilise the economy whereas the others do not. ii. Monetarists believe that monetary policy is more effective than fiscal policy in eliminating unemployment, whereas Keynesians believe the opposite. iii. Supply-siders believe that incentives to work, save and invest are more important than macroeconomic demand manipulation in managing the economy. iv. The classical economists believed that the monetary and real sides of the economy wereentirely separate, whereas the other schools believe that the monetary sector can affecthe real economy, at least in the short run. a) i b) i and ii c) i, iii and iv d) ii, iii and iv