Verify that the vector $X_p$ is a particular solution of the given nonhomogeneous linear system.
$X' = \begin{pmatrix} 2 & 1 \\ 1 & -1 \end{pmatrix} X + \begin{pmatrix} -9 \\ 6 \end{pmatrix}$; $X_p = \begin{pmatrix} 1 \\ 7 \end{pmatrix}$
Writing the system in the form $X' = AX + F$ for some coefficient matrix A and vector F, one obtains the following.
$X' = \begin{pmatrix} \Box & \Box \\ \Box & \Box \end{pmatrix} X + \begin{pmatrix} \Box \\ \Box \end{pmatrix}$
For $X_p = \begin{pmatrix} 1 \\ 7 \end{pmatrix}$, one has
$X'_p = \begin{pmatrix} \Box \\ \Box \end{pmatrix}$
$AX_p + F = \begin{pmatrix} \Box \\ \Box \end{pmatrix}$
Since the above expressions ---Select---, $X_p = \begin{pmatrix} 1 \\ 7 \end{pmatrix}$ is a particular solution of the given system.
