Question

Find the standard matrix of T_1 ° T_2 : R^2 → R^2 where
T_1 : R^2 → R^2 is anticlockwise rotation about the origin by π/3 radians, and
T_2 : R^2 → R^2 is reflection about the line x=0.

Answer 1

Given by T2T1 where

T2 is ((cos x,-sinx)(sinx cos x)) x= pi/3 and
T1 is ((cos 2y,sin 2y)(sin2y -cos 2y)) y=0

Answer 2

You also need to compose the two matrices after you set them up

Answer 3

Also it looks like your T2 is a clockwise rotation, it should be counterclockwise

Answer 4

\[A_{T_1} = \left[ \begin {array}{cc} \cos \left( \frac{\pi}{2} \right) &-\sin \left(
\frac{\pi}{2} \right) \\ \sin \left( \frac{\pi}{2}\right) &\cos
\left( \frac{\pi}{2} \right) \end {array} \right]\]\[A_{T_2}=\left[ \begin {array}{cc} 1&0\\ 0&-1\end {array}
\right] \]\[A_{T_1}A_{T_2} = \left[ \begin {array}{cc} \cos \left( \frac{\pi}{2} \right) &-\sin \left(
\frac{\pi}{2} \right) \\ \sin \left( \frac{\pi}{2}\right) &\cos
\left( \frac{\pi}{2} \right) \end {array} \right]\left[ \begin {array}{cc} 1&0\\ 0&-1\end {array}
\right] \]

Answer 5

((cos x,-sinx)(sinx cos x)) is the same as above so I don't know what u r are talking about...

Answer 6

Oh sorry I was interpreting them as columns not rows

Answer 7

As for the composition if T1 and T2 are the transformations then T2 composed with T1 is represented by matrix T2T1.

Answer 8

In the standard notation they should be interpreted as columns not rows.

Answer 9

That's why I bracketed them, same as Wolfram.

Answer 10

jim help me i post prob