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

MATH152 April 2017
Other MATH152 Exams

Question B 06 (a)

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

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

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

(a) Find all eigenvalues and a basis of eigenvectors of ${\displaystyle A}$

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