Question

PLEASE HELP HELP HELP!!
Use matrices to rotate the vector v =(-4,1) = by 270º. Write the resulting vector in component form.

Answer 1

The formula for the rotational matrix is:
\[R=\left[\begin{matrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{matrix}\right]\]
for 270 degrees, this becomes:
\[R=\left[\begin{matrix}0 & 1 \\ -1 & 0\end{matrix}\right]\]
then multiply this times the vector (-4,1)
So:
\[\left[\begin{matrix}0 & 1 \\ -1 & 0\end{matrix}\right]\left(\begin{matrix}-4 \\ 1\end{matrix}\right)=\left(\begin{matrix}1 \\ 4\end{matrix}\right)\] or (1,4)