Tagged: matrix power

How to Obtain Information of a Vector if Information of Other Vectors are Given

Problem 688

Let $A$ be a $3\times 3$ matrix and let
\[\mathbf{v}=\begin{bmatrix}
1 \\
2 \\
-1
\end{bmatrix} \text{ and } \mathbf{w}=\begin{bmatrix}
2 \\
-1 \\
3
\end{bmatrix}.\] Suppose that $A\mathbf{v}=-\mathbf{v}$ and $A\mathbf{w}=2\mathbf{w}$.
Then find the vector
\[A^5\begin{bmatrix}
-1 \\
8 \\
-9
\end{bmatrix}.\]

 
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