MATH 1553 Midterm: MATH 1553 GT s Exam3
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Gt username: no books or notes are allowed, all calculators and/or electronic devices are not allowed, show all work and fully justify your answer to receive full credit, please box your answers, good luck! 1: find all eigenvalues of the matrix. (15 pts. ) R2 be the linear transformation which rst rotates vectors in r2 by 180 , and then projects the result to the x-axis. Find two linearly independent eigenvectors of the standard matrix of t and state the associated eigenvalues. (10 pts. ) 2: find all complex eigenvalues of the matrix a, and nd an associated eigenvector for each (10 pts. ) eigenvalue. 2: let a be a 2 2 matrix which satis es av1 = 2v1 and av2 = v2 where v1 = (cid:20)3. If x is the vector x = (cid:20)7. 3: the matrix a = (cid:20)a b a(cid:21) has eigenvalues = a + b and = a b.
