Answer True or False. 1. In motion means moving. 2. Scientists do not use a frame of reference to talk about motion.

Gegeben sind die Matrizen \( A=\left[\begin{array}{ll}2 & -4 \\ 0 & -1\end{array}\right], B=\left[\begin{array}{cccc}-2 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right], C=\left[\begin{array}{lll}0 & 4 & 7 \\ 0 & 2 & 2 \\ 0 & 0 & 0\end{array}\right], D=\left[\begin{array}{ccc}-4 & 0 & 4 \\ 9 & -7 & 8 \\ 0 & -3 & 9\end{array}\right], E=\left[\begin{array}{ccc}-4 & 0 & 0 \\ -6 & 0 & 0\end{array}\right] \), \( \operatorname{Bestimmen} \) Sie jeweils den Rang und entscheiden Sie, ob die Inverse existiert und berechnen Sie gegebenenfalls, \( \operatorname{rang}(A)=\square \) \( \operatorname{rang}(B)=\square \) \( \operatorname{rang}(C)=\square \) \( \operatorname{rang}(D)=\square \) \( \operatorname{rang}(E)=\square \)

Con la Notación Cientifica se representan números muy... A. Muy Grandes B. Muy Pequeños C. Muy grandes y muy pequeños

List all the given numbers that are (a) integers, (b) rational numbers, (c) irrational numbers, (d) real numbers, and (e) imaginary numbers. \[ 9, \sqrt{-16}, \frac{\sqrt{2}}{4},-2,-\frac{\pi}{2}, \frac{1}{6},-\sqrt{-7},-2.99 \]

Es sei \( B_{1}=\left\{\dot{e}_{1}, \dot{e}_{2}, \dot{e}_{3}\right\} \) die Standardbasis des \( \mathbb{R}^{3} \) und \( B_{2}=\left\{\dot{v}_{1}, \dot{v}_{2}, \dot{v}_{3}\right\} \) die Basis mit \[ \dot{v}_{1}=\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right], \dot{v}_{2}=\left[\begin{array}{l}0 \\ 0 \\ 4\end{array}\right], \dot{v}_{3}=\left[\begin{array}{c}3 \\ 0 \\ -3\end{array}\right] \] Weiter sei die lineare Abbildung \( f: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \) durch die folgenden Bilder gegeben \[ f\left(\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]\right)=\left[\begin{array}{c}1 \\ -6 \\ 1\end{array}\right], f\left(\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]\right)=\left[\begin{array}{c}0 \\ 5 \\ -2\end{array}\right], f\left(\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]\right)=\left[\begin{array}{c}2 \\ -1 \\ 4\end{array}\right] \] a) Berechnen Sie \( f_{B_{1}, B_{1}} \)

Ejemplo 4 Encuentre los valores y vectores propios de la matriz \[ A=\left(\begin{array}{lll}2 & 1 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right) \] Solución.