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for E = 4 I drew in Matlab. -3 2 2 P Figure 1: Graph of ε 4 This is an ellipse. (a) (5 points) Let the SVD of E be E = UΣVT. Show indeed the graph of & is an ellipse with semi-major axis σ₁ and semi-minor axis σ2. What are the coordinates of the two vertices on the major axis (i.e., points A and B in the plot) and what are the coordinates of the two vertices on the minor axis (i.e., points C and D)? (b) (3 points) Draw the same plot as I did. Hints: 1. Use the SVD of E to find an equation w=UTy satisfies. From the form of the equation you can conclude the graph in terms of wis an ellipse with semi-major axis σ₁ and semi-minor axis σ. Then argue why the graph in terms of y = Uw is an ellipse with semi-major axis σ₁ and semi-minor axis σ2. 2. There are two ways to draw the graph of ε. One way is to use the fact that any ЄR² with ||||2 = 1 can be written as [cos(6), sin(e)] and different leads to different x, resulting in different y. After you get many points for y for 0 € [0,2], you can use plot to draw the graph. The other way is to use explot to draw the equation y satisfies. To draw the major and minor axes, you can use line and to draw the four vertices you can use text.

Fig: 1