Question

Find the matrix P that multiplies (x; y; z) to give (y; z; x). Find the matrix Q that multiplies (y; z; x) to bring back (x; y; z).

Answer 1

Answer:

$P = \left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right]$

$Q = \left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right]$

Step-by-step explanation:

$P*\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}0&1&0\\0&0&1\\1&0&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}y\\z\\x\end{array}\right]$

$Q*\left[\begin{array}{c}y\\z\\x\end{array}\right]=\left[\begin{array}{ccc}0&0&1\\1&0&0\\0&1&0\end{array}\right] \left[\begin{array}{c}y\\z\\x\end{array}\right] = \left[\begin{array}{c}x\\y\\z\end{array}\right]$