Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 06 (a)/Statement

The matrix A below represents a transformation that reflects vectors in $\mathbb {R} ^{3}$ in a plane $P$ that contains the origin.

${\begin{bmatrix}1/3&2/3&-2/3\\2/3&1/3&2/3\\-2/3&2/3&1/3\end{bmatrix}}$

Note: you can use geometric insight to greatly simplify the calculations below.

(a) Find all eigenvalues and a basis of eigenvectors of $A$