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Determine whether -105° and -465° are co-terminal angles. Justify your answer fully.
Determine whether -105° and -465° are co-terminal angles. Justify your answer fully.
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
Problem 2. Determine whether the sequence { "" } converges or diverges. Justify your answer.
2. Determine whether the following equations are linear in r, y and z: justify your answer.
Determine whether the multiplicative group Z∗24 is cyclic or not. Show work to justify your answer.
5. Determine whether or not matrix A shown below is orthogonal and justify your answer. 0 -21 A = 10 INOMI- 1 0 0 1
5. Determine whether or not matrix A shown below is orthogonal and justify your answer. 0 -2 15 A= 0 0 1 nl N 0 1
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
Determine whether each of the following algorithms is fully correct, and prove that your answer is correct. Determine whether each of the following algorithms is fully correct, and prove that your answer is correct. 4 5 (a) [10 points) A(2) IN :TER,r> 1 1 r'= 2 p=0 3 while r'> 1 do p=p+1 r' = 2/2 6 return p OUT: p = log2 (b) [10 points) B(2) IN : r ER, 1 > 1 1 while r > 1 do...
5. Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation S on R given by xSy if and only if X – Y E R – N is an equivalence relation.
Question 1 (15 points) (a) Determine whether the following extensions are normal. Justify your answer. (1) Q CQ(V2, 92). (2) F = F3(t) C F(a), where t is a variable and a is a root of x3 – t in the splitting field. (b) Give an example of a normal extension of Q that is not finite. Justify your answer.