Question

Use matrix multiplication to find the image of v=(-2,1,2) when it is rotated through ‎an angle of θ=-π/4 radians about the y-axis

Answer 1

i know it has something to do with trig .... i just cant recall it at the moment

Answer 2

class is starting, linear algebra :) ill try to chk this back in abt 2 hours.

Answer 3

The matrix rotation is
\[A=\left( \begin{array}{ccc}
\cos(\theta)& 0& \sin(\theta) \\
0 &1 &0 \\
- \sin(\theta) & 0 & \cos(\theta) \\
\end{array} \right)
\]
Use
\[\theta= -\frac \pi 4
\]
and Multiply A by the transpose of of
(-2,1,2)

Answer 4

This a evaluated at -\pi/4
\[
\left(
\begin{array}{ccc}
\frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{2}} \\
0 & 1 & 0 \\
\frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\
\end{array}
\right)
\]
Multiply it by
\[
\left(
\begin{array}{c}
-2 \\
1 \\
2 \\
\end{array}
\right)
\]
to get
\[\left(
\begin{array}{c}
-2 \sqrt{2} \\
1 \\
0 \\
\end{array}
\right)
\]

Answer 5

thanks alot