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Diagunabisable the matrix \( A=\left[\begin{array}{ccc}8 & -8 & -2 \\ 4 & -3 & -2 \\ 3 & -4 & 1\end{array}\right] \) and find \( A^{4} \)

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1 Answer

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by (38.9k points)

A = \(\begin{bmatrix}8&-8&-2\\4&-3&-2\\3&-4&1\end{bmatrix}\) 

A2\(\begin{bmatrix}8&-8&-2\\4&-3&-2\\3&-4&1\end{bmatrix}\)\(\begin{bmatrix}8&-8&-2\\4&-3&-2\\3&-4&1\end{bmatrix}\) = \(\begin{bmatrix}26&-32&-2\\14&-15&-4\\11&-16&3\end{bmatrix}\)

A4 = A2. A2 = \(\begin{bmatrix}26&-32&-2\\14&-15&-4\\11&-16&3\end{bmatrix}\)\(\begin{bmatrix}26&-32&-2\\14&-15&-4\\11&-16&3\end{bmatrix}\)

\(\begin{bmatrix}206&-320&-70\\110&-159&20\\95&-160&51\end{bmatrix}\)

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