Answer:
The Matrix of T is
[tex]\left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\-sin(\pi/6)&-cos(\pi/6)\end{array}\right][/tex]
Step-by-step explanation:
Rotate -pi/6 Clockwise is the same as rotating pi/6 anticlockwise. The matrix of that rotation is
[tex]\left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\sin(\pi/6)&cos(\pi/6)\end{array}\right][/tex]
The matrix of the reflection through the x1-axis is
[tex]\left[\begin{array}{cc}1&0\\0&-1\end{array}\right][/tex]
Therefore, the composition is the product of both matrices is the matrix of T
[tex]MT = \left[\begin{array}{cc}1&0\\0&-1\end{array}\right] * \left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\sin(\pi/6)&cos(\pi/6)\end{array}\right] = \left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\-sin(\pi/6)&-cos(\pi/6)\end{array}\right][/tex]
I hope that works for you!
