Interpret each of the following linear mappings geometrically, as in Problems 1 and 2:a) y...

Interpret each of the following linear mappings geometrically, as in Problems 1 and 2:

a) y = Ex.

b) y = Mx.

Problem 1

Let the linear mapping T have the equation y = Cx. For general x, find the angle between x and T(x) = y, as vectors in V2, and also compare |x| and | T(x)|. From these results, interpret T geometrically. [Hint: Consider x as and y as where O is the origin of E2 and P and Q are points of E2.]

Problem 2

Let the linear mapping T have the equation y = Dx. Regard x as as in Problem, and describe geometrically the relation between x and y = T(x).