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Name: CSU ID: Homework 8 March 27, 2015 16 1. Suppose that T is a linear operator. Find T 24 given that 1 −2 −1 T 4 = 3 , 0 0 −7 1 T 1 = 2 8 −4 2. S5.1 ]6(d), ]10 3. S5.1 ]12 4. S5.1 ]14 5. S5.1 ]20(a,c,e) 6. S5.1 ]24 7. S5.1 ]34 8. S5.1 ]36 9. The eigenvalues of A given below are λ = 3, −2, 6. Find the eigenvectors and, if possible, define them in terms of integers. Define an S and S −1 such that S −1 AS = diag(3, −2, 6) (diag(a, b) refers to a 2 × 2 diagonal matrix with a and b on the main diagonal.) −36 126 97 A = 12 −30 −26 −30 90 73 *** For the problems listed below, we will know on Wednesday if they should be turned in with homework on Friday. If not, you should still expect S5.2 to be covered on Exam 2. 10. S5.2 ]20 11. S5.2 ]27 12. S5.2 ]32 1 −7 T 2 = 0 0 −3