Question: Let T be a positive definite 2 2 matrix. Let En = (Tnx | ||x|| = 1], n = 0, 1,2.......be the image of

Let T be a positive definite 2 × 2 matrix. Let En = (Tnx | ||x|| = 1], n = 0, 1,2.......be the image of the unit circle under the nth power of T.
(a) Prove that En is an ellipse.
True or false:
(b) The ellipses En all have the same principal axes.
(c) The semi-axes are given by rn = rn1 sn = sn1.
(d) The areas are given by An = πan where α = A1/π.

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