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?