Tagged: orthonormal

Problem 218

For a real number $0\leq \theta \leq \pi$, we define the real $3\times 3$ matrix $A$ by
$A=\begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta &\cos\theta &0 \\ 0 & 0 & 1 \end{bmatrix}.$

(a) Find the determinant of the matrix $A$.

(b) Show that $A$ is an orthogonal matrix.

(c) Find the eigenvalues of $A$.