1. ## Matrix Transformations Help

Sorry I'm new to this topic and attempting to self teach can anyone give me an idiots guide to this question

The Matrix $\displaystyle \begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0\end{bmatrix}$ represents a rotation.

Find the equation of the axis of rotation and what is the angle of the rotation

many thanks

Simon

2. Hello,

The axis is generated by the eigenvector associated to the eigenvalue 1.

$\displaystyle AX=X$

$\displaystyle \begin{pmatrix} 0&1&0 \\ 0&0&1 \\ 1&0&0 \end{pmatrix} \begin{pmatrix} x_1\\x_2\\x_3 \end{pmatrix}=\begin{pmatrix} x_1\\x_2\\x_3 \end{pmatrix}$

Solve for $\displaystyle x_1, ~x_2, ~x_3$

hmmm I'm sorry I don't remember how to find the angle >.<

3. This questions requires a decent 3D drawing.

Notice that $\displaystyle \begin{pmatrix} 0&1&0 \\ 0&0&1 \\ 1&0&0 \end{pmatrix} \begin{pmatrix} i\\j\\k \end{pmatrix}=\begin{pmatrix} k\\i\\j \end{pmatrix}$

Your swapping the axis around in order, so the line must be $\displaystyle \begin{pmatrix} 1\\1\\1 \end{pmatrix}$ and the angle is 120 degrees (as $\displaystyle A^3 = I$ )

Bobak