Answer to Question #22656 in Matrix | Tensor Analysis for Craig

Question

Let f be the linear transformation represented by the matrix

M = (0 3)
(1 −1)

(a) State what effect f has on areas, and whether f changes orientation.

(b) Find the matrix that represents the inverse of f.

(c) (i) Use the matrix that you found in part (b) to find the image f(C) of the unit circle C under f, in the form;

ax^2 + bxy + cy^2= d,

where a, b, c and d are integers.

(ii) What is the area enclosed by f(C)?