Please show some work in all of your problems so that we get the idea you have actually tried them.
Consider the linear transformation T: R^3->R^3 which acts by rotation around the y-axis by an angle of pi, followed by a shear in the x-direction by a factor of 2.
a) Find the matrix for T. Explain your method.
b) What is T(1,2,3)
c) Without calculation, explain whether the matrix you found in a) is invertible. What is the transformation corresponding to the inverse?
it's a pretty straightforward question if you've covered linear transformations at all.
a 3x3 rotation matrix about say the Z axis, of rotation angle $\theta$ is
$R_{\theta}=\left(\begin{array}{ccc}\cos(\theta) &\sin(\theta) &0 \\ -\sin(\theta)&\cos(\theta) &0\\ 0 &0 &1\end{array}\right)$
that sort of thing must be in your book somewhere.
a shear matrix in the Z direction of shear factor $\lambda$ is
$S_{\lambda}=\left(\begin{array}{ccc}1 &0 &0 \\ 0 &1 &0 \\ 0 &0 &\lambda \end{array}\right)$
again that's got to be in your book.
take another look