one last question...
I have been given two questions, both of which i ahve no clue on what to do
linear transformation T : R^2-->R^2 with standard matrix M=[a,0;0,b] a>b>0
a) show the circle x^2+y^2=r^2 is transformed by T to the ellipse:
hint, let P(rcos(theta), rsin(theta)) be a point on the circle and show that P is transformed to Q(arcos(theta), brsin(theta)), a point on the ellipse.
b)derive a formula for the area of an ellipse
a) Find the image of in the following way:
Originally Posted by deragon999
Let X be the column matrix . Calculate MX .....
b) If you operate on an object with a linear transformation, the area of the image is the original area multiplied by the determinant of the matrix of the linear transformation.
Consider the circle of radius r = 1. The area of this circle is pi.
Transform this circle into an ellipse of major and minor axes 2a and 2b. Then the area of this ellipse is pi det(M) = pi ab ......