(Solved): 6. Let R be the linear transformation on two-dimensional real vectors that multiplies the vector co ...

6. Let $R$ be the linear transformation on two-dimensional real vectors that multiplies the vector components by 2 . Let $S$ be the linear tranformation which projects vectors onto the first coordinate (i.e., the $x$-axis). Let $T$ be the linear transformation which rotates a vector by $?/2$ radians. a) Write a matrix for the composite linear tranformation which performs $R$, then $S$, then $\mathrm{T}$ (in that order) b) Use your answer to the previous part to compute the image of the vector $\mathbf{u}=\left[\begin{array}{c}?3\\ 4\end{array}\right]$ under this composite tranformation. c) Is the composite transformation injective (one-to-one)? You may give your answer in clear English if you feel that no calculation is necessary.