Question

By which matrix should you multiply vector [1 3] to rotate it 180°?

Answer 1

Answer:

B

Step-by-step explanation:

Rotation 180° is accomplished by negating both the x- and y-coordinates. That is, you multiply each of them by -1. You want the opposite of the identity matrix, so matrix B.

Answer 2

We have that the Rotation of matrix $Matrix =\begin{pmatrix}1 \\3\end{pmatrix}$ will be rotated 180 degree if $Matrix =\begin{pmatrix}1 \\3\end{pmatrix}$ is multiplied by $\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}$  

Option D is correct

From the Question we are given

$Matrix =\begin{pmatrix}1 \\3\end{pmatrix}$

it is important to note that the rotation of the identity matrix  $\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}$ rotating across the Cartesian co-ordinate is a $180 \textdegree$ is going to give a matrix   $\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}$  

Therefore

The Rotation of matrix $Matrix =\begin{pmatrix}1 \\3\end{pmatrix}$ will be rotated 180 degree if $Matrix =\begin{pmatrix}1 \\3\end{pmatrix}$ is multiplied by $\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}$  

Option D is correct

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