MATH 3A Final: Final_3A
2
MATH 3A Full Course Notes
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There are 7 exercises, worth a total of 90 points. Provide computations and or explanations, unless stated otherwise. You can leave expressions such as 5 32019. (hint: diagonalize a). 1 + 22018 1 + 22019 (cid:21) . Exercise 2 (15 = 4 + 4 + 3 + 2 + 2 pts) 0 0 0 6 (a) compute the characteristic polynomial of a and show that the eigenvalues of. Solution: (a) 2( 6)2. (b) e0 has basis {[ 2, 1, 0, 0]t , [ 3, 0, 1, 0]t}. E6 has basis {[1, 1, 1, 0]t , [0, 0, 0, 1]t}. (c) yes, d = diag(0, 0, 6, 6) and. 0 (d) yes, since 1 is not an eigenvalue (you can plug in = 1 in a). (e) yes, same p , but with d = diag(1, 1, 7, 7). Exercise 3 (15 = 5 + 5 + 5 pts)
