## Solve a System by the Inverse Matrix and Compute $A^{2017}\mathbf{x}$

## Problem 300

Let $A$ be the coefficient matrix of the system of linear equations

\begin{align*}

-x_1-2x_2&=1\\

2x_1+3x_2&=-1.

\end{align*}

**(a)** Solve the system by finding the inverse matrix $A^{-1}$.

**(b)** Let $\mathbf{x}=\begin{bmatrix}

x_1 \\

x_2

\end{bmatrix}$ be the solution of the system obtained in part (a).

Calculate and simplify

\[A^{2017}\mathbf{x}.\]

(*The Ohio State University, Linear Algebra Midterm Exam Problem*)

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