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

Similar Questions
    1. answers icon 0 answers
  1. Let T1: P1 -> P2 be the linear transformation defined by:T1(c0 + c1*x) = 2c0 - 3c1*x Using the standard bases, B = {1, x} and B'
    1. answers icon 0 answers
  2. Let f be the linear transformation represented by the matrixA=(-2 3 4 -4) a=-2, b=3, c=4, d=-4 Find the point (x,y) such that
    1. answers icon 1 answer
  3. Hi! I need help with these two questions. Thanks! :)1.) Can we multiply the Matrix A (which is 3 x 4 matrix) by the other
    1. answers icon 2 answers
more similar questions