(Solved): Use diagonalisation to calculate the matrix exponential \( A^{4} \) for the f ...

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Use diagonalisation to calculate the matrix exponential \( A^{4} \) for the following matrix: \[ A=\left(\begin{array}{cc} 4 & -1 \\ 2 & 1 \end{array}\right) \] Select the correct exponential from the list (hint: diagonalisation!): \[ \begin{array}{l} \left(\begin{array}{cc} 256 & 1 \\ 16 & 1 \end{array}\right) \\ \left(\begin{array}{cc} 146 & 130 \\ -65 & -49 \end{array}\right) \\ \left(\begin{array}{cc} 1 & 16 \\ 1 & 256 \end{array}\right) \\ \left(\begin{array}{cc} 146 & -65 \\ 130 & -49 \end{array}\right) \end{array} \]