1.The projection P: 3 2 is defined by induced by a matrix and find the matrix. 2.Let T: 3 for all in 3 . Show that P is 3 be a transformation. show that T is induced by a matrix and find the matrix. T is a reflection in the xy plane. 3.Suppose AB = 0, where A and B are square matrices. Show that: a If one of A and B has an inverse, the other is zero. b .(BA)2 = 0. 4.Let T : 3 2 be a linear transformation. a Find if and 5.In each case use Theorem 2 to obtain the matrix A of the transformation T. You may assume that Tis linear in each case. a T: 3 3 is reflection in the xz plane. 6.In each case show that T: 2 2 is not a linear transformation. a Express reflection in the line y = x as the composition of a rotation followed by reflection in the liney = x. 8. In each case find the matrix of T: 3 3: a T is rotation through about the x axis (from the y axis to the z axis). 9.Given c in , define Tc: n by Tc(x) = cx for all x in transformation and find its matrix. 10. n . Show that Tc is a linear \f\f