Question

Can anyone please help me with this question:

Using Matrices to rotate the vector V= (-4,1) = by 270°. Write the resulting vector in component form.

Answer 1

@wio Can you pls help me?

Answer 2

Do you remember the rotation matrix?

Answer 3

kind of

Answer 4

\[
\begin{bmatrix}
\cos\theta & -\sin\theta \\
\sin\theta & \cos\theta
\end{bmatrix}
\]Multiply this by a vector to rotate it \(\theta\) degrees.

Answer 5

can you show me how to do that?

Answer 6

First, \(\theta = 270^\circ \) so: \[
\begin{bmatrix}
\cos(270^\circ) & -\sin(270^\circ)\\
\sin(270^\circ) & \cos(270^\circ)
\end{bmatrix}
=
\begin{bmatrix}
0 & 1\\
-1 & 0
\end{bmatrix}
\]

Answer 7

Multiply \[
\begin{bmatrix}
0 & 1\\
-1 & 0
\end{bmatrix}
\begin{bmatrix}
-4\\
1
\end{bmatrix}
\]

Answer 8

Im sorry I left and took long. My computer just crashed.

anyways it'll be:

[1]
[4]

Answer 9

IS that it or do i need to do more steps?

Answer 10

@wio

Answer 11

Yeah, that is the answer. Just graph to check.

Answer 12

Thank you so much wio!