2 20 Let A = Which of the following is a consequence of the Cayley -Hamilton Theorem? 2 10 L-10 0] OD A 3 +A² – 6A +1=0. O E. A3+A² - 6A =0. O C. 43 – 6AI=0. AS=6A =0. A. 6AI=0.

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Q: Find simpler expressions for the quantities in Exercises 45–48.

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Q: 11. Let S= {| -2 }. Show that u= E span S. 1 2

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Q: 4. Prove: AL = CM C Key steps of proof: a. AABD = ACDB b. AD = CB; Z1 = Z 2 c. AADL = ACBM M A B. d.…

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Q: o.10. Prove that (a) J,"(x) = ¿[J,(x) – 2J,(x) + J, + glw). n n-2 n' n+2

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Q: 3. Let A = {3k : k € Z} and B = {15m + 12n : m, n € Z}. Prove that A = B.

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Q: 9. Prove or disprove. (a) Vn e Z*, n² < 2". (b) Vm e Z, if m is odd, then m² is odd.

A: In this question we have prove if this equation are valid or not.

Q: (ii) Prove the following Frenet-Serret formulae: T = KUN, N-KUT+TU B.

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Q: 4|5" – 1, Vn e N

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Q: 9. Let S- {xeZ| 3r.seZ,x=9r+6s) and T={xeZ| 3x} b) Prove that T Cs. a) Prove that SCT. Hint for (b):…

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