Quantitative Finance

Matrix Exponentiation

What is $\exp(A)$ if $\displaystyle A=\begin{pmatrix} 8 & 1 \\ 1 & 8 \end{pmatrix} ?$

$\begin{matrix} \text{(A)} \quad { \frac{1}{2}\begin{pmatrix}e^{9}+e^{7} & e^{9}-e^{7} \\ e^{9}-e^{7} & e^{9}+e^{7} \end{pmatrix} } & \text{(B)} \quad { \frac{1}{2}\begin{pmatrix}e^{9}-e^{7} & e^{9}+e^{7} \\ e^{9}+e^{7} & e^{9}-e^{7} \end{pmatrix} } \\ \\ \text{(C)} \quad { \frac{1}{4}\begin{pmatrix}e^{9}+e^{7} & e^{9}-e^{7} \\ e^{9}-e^{7} & e^{9}+e^{7} \end{pmatrix} } & \text{(D)} \quad { \frac{1}{4}\begin{pmatrix}e^{9}-e^{7} & e^{9}+e^{7} \\ e^{9}+e^{7} & e^{9}-e^{7} \end{pmatrix} } \end{matrix}$

What is $\exp(A)$ if $\displaystyle A=\begin{pmatrix} 1 & 7 \\ 0 & 1 \end{pmatrix} ?$

What is $\exp(A)$ if $\displaystyle A=\begin{pmatrix} 4 & 0 \\ 0 & 7 \end{pmatrix} ?$

What is $\exp(A)$ if $\displaystyle A=\begin{pmatrix} 9 & 0 & 0 \\ 5 & 4 & 0 \\ 5 & 1 & 3 \end{pmatrix}?$

What is $\exp(A)$ if $\displaystyle A=\begin{pmatrix} 0 & -8 \\ 0 & 8 \end{pmatrix} ?$

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