Find the matrix that represents a rotation clockwise around the origin by 30∘ followed by a magnification by a factor of 4.
My attempt:
I multiplied the magnification matrix $\left[ {\begin{array}{cc}
4 & 0 \\
0 & 1 \\
\end{array} } \right]$ by the rotation matrix of $-30$ degree, $\left[ {\begin{array}{cc}
\cos(t) &-\sin(t) \\
\sin(t) & \cos(t \\
\end{array} } \right]$ where $t=\theta$.
Best Answer
The problem with this is that $[\{4\;0\};\{0\;1\}]$ is not a scaling matrix, it is a "stretching" matrix, only stretching vectors in the x direction. What you are looking for is $[\{4\;0\};\{0\;4\}]$. Upon multiplying these together, we get $[\{4\cos(-30^{\circ})\;\;-4\sin(-30^{\circ})\};\{4\sin(-30^{\circ})\;\;4\cos(-30^{\circ})\}]$, or $[\{2\sqrt{3}\;\;-2\};\{2\;\;2\sqrt{3}\}].$