Let T be an invertible linear transformation from ℝ 2 to ℝ 2. Show that the image of the...

Let T be an invertible linear transformation from ℝ ² to ℝ ². Show that the image of the unit circle is an ellipse centered at the origin.8 Hint: Consider two perpendicular unit vectors are perpendicular. See Exercise 47. The unit circle consists of all vectors of the form

where t is a parameter.