I am trying to solve the following matrix equation.
$$X \begin{pmatrix} a \\ b \\c \end{pmatrix} = \begin{pmatrix} b \\ c \\a \end{pmatrix}$$
My analysis:
- $X$ must be 3 by 3 matrix.
- $X=\begin{pmatrix} b \\ c \\a \end{pmatrix} \begin{pmatrix} a \\ b \\c \end{pmatrix}^{-1}$
Question
How can I calculate $ \begin{pmatrix} a \\ b \\c \end{pmatrix}^{-1} $?