Let A = _ 1 1 0 2 _ (a) Find Ax when x = _ 1 1 _ . Graph both x and Ax in the same
Chapter 9, Problem 1(choose chapter or problem)
Let A = _ 1 1 0 2 _ (a) Find Ax when x = _ 1 1 _ . Graph both x and Ax in the same coordinate system. (b) Find the eigenvalues 1 and 2, and the corresponding eigenvectors u1 and u2, of A. (c) If ui is the eigenvector corresponding to i , find Aui and explain graphically what happens when you apply A to ui . (d) Write x as a linear combination of u1 and u2; that is, find a1 and a2 so that x = a1u1 + a2u2 Show that Ax = a11u1 + a22u2 and illustrate this equation graphically.
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