Let 0 € (0,2) Let T: F? → F2 via: 21 21 T (3) 1 where A= cos - sin sin cos e . If F= C, find the eigenvalues and eigenve

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Let 0 0 2 Let T F F2 Via 21 21 T 3 1 Where A Cos Sin Sin Cos E If F C Find The Eigenvalues And Eigenve 1 (36.65 KiB) Viewed 19 times

Let 0 € (0,2) Let T: F? → F2 via: 21 21 T (3) 1 where A= cos - sin sin cos e . If F= C, find the eigenvalues and eigenvectors of T. Hint: Use the identity cos? + sin0 = 1 • If F=R, this transformation is the counterclockwise rotation of the vector (21, 22) about the origin by the angle . What angles should be if T is to have real eigenvalues? 4 Find all eigenvalues of the following matrix, and then find a corre- sponding eigenvector for each. A= 10 1 -13-2 5 Let i= -2 and y = 2 5 Find proj (7)