(Solution) - Use the command eigshow A to apply the eigshow utility to -(2025 Original AI-Free Solution)

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Use the command eigshow(A) to apply the eigshow utility to the matrix A. Click on the eig/(svd) button to switch into the svdshow mode. The display in the figure window should show a pair of orthogonal vectors x, y and their images Ax and Ay. Initially, the images of x and y should not be orthogonal. Use the mouse to rotate the x and y vectors counterclockwise until their images Ax and Ay become orthogonal. When the images are orthogonal, x and y are right singular vectors of A. When x and y are right singular vectors, how are the singular values and left singular vectors related to the images Ax and Ay? Explain. Note that when you rotate a full 360° the image of the unit circle traces out as an ellipse. How do the singular values and singular vectors relate to the axes of the ellipse?