Explain the difference between exponential growth and exponential decay.

16. Sea \( A \in \mathcal{L}\left(\mathbf{R}^{3}\right) \) cuya matriz con respecto a la base canónica es \[ A=\left(\begin{array}{rrr}0 & x & 2 \\ -2 & 0 & -2 \\ 2 & -2 & 0\end{array}\right) \] con \( x \in \mathbf{R} \). a) Encontrar \( x \) pará que \( A \) sea diagonalizable.

X. Esercizio 13.10 Trovare, se esiste, un'applicazione lineare \( F: \mathbb{R}^{2} \longrightarrow \mathbb{R}^{3} \) tale che \[ F(1,1)=(1,-1,-1) \quad F(-1,-1)=(-1,1,1) \quad F(1,0)=(1,0,-3) \] È unica tale applicazione?

16. Sea \( A \in \mathcal{L}\left(\mathbf{R}^{3}\right) \) cuya matriz con respecto a la base canónica es \[ A=\left(\begin{array}{rrr}0 & x & 2 \\ -2 & 0 & -2 \\ 2 & -2 & 0\end{array}\right) \] con \( x \in \mathbf{R} \). a) Fncontrar \( x \) para que \( A \) sea diagonalizable.

7.Soru Tek bir değişkene ilişkin oransal değişimleri gösteren endekse ne ad verilir? A Bileşik endeks B Sabit esash endeks C Basit endeks D Zaman endeksi E Mekân endeksi

Uestion vo 3\( \} \) Examine whether the following set of vectors is a Basis and if so fint imensions of the Vector Space \( \mathrm{B}=\left\{\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right],\left[\begin{array}{ll}0 & 0 \\ 0 & 1\end{array}\right]\right\} \) of Vector Space of all \( 2 \times 2 \) diagonal matrices