Question

Matrix transformations- please help?
let f be the linear transformation represented by the matrix

M = (4 2)
.......(0 -2)

a) state what effect f has on areas and whether it changes orientation

b) Find the matrix that represents the inverse of f

c) Use the matrix 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, d are integers

d) what is the area enclosed by f(c)?


My answers;

a)det M = (4*-2) - (2*0) = -8 so f scales areas by factor 8 and changes orientation

b) m^-1 = 1/-8 (-2 -2) ... (1/4 1/4)
..............=..............o 4) = (0 -1/2)


c) 1/16x^2 + 2/16xy + 1/16y^2 = 1
which is;

x^2 + 2xy + y^2 = 16

(ive struggled with this one so if its wrong i would appreciate some help with my working out)

d) the area enclosed by f(C) is 16pi


Thanks