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For problems and = (pants . and €) , YOU are given (WO functions_ fn) and _ E(n) Determine whether fln) is O(g(n)) Or nOL Show that it is Or nol, using the te...

Question

For problems and = (pants . and €) , YOU are given (WO functions_ fn) and _ E(n) Determine whether fln) is O(g(n)) Or nOL Show that it is Or nol, using the techniques from class For part b, determine whether fln) O(gln) ) and show why IS Or IS nOL.An) = 2 , S(n) = 2" +#For the funetions partthat An) is ((g(n))? Show #hy or why noLfn) =s(n) =_

For problems and = (pants . and €) , YOU are given (WO functions_ fn) and _ E(n) Determine whether fln) is O(g(n)) Or nOL Show that it is Or nol, using the techniques from class For part b, determine whether fln) O(gln) ) and show why IS Or IS nOL. An) = 2 , S(n) = 2" +# For the funetions part that An) is ((g(n))? Show #hy or why noL fn) = s(n) =_



Answers

For a sequence $\left\{a_{n}\right\}$ the terms of even index are denoted by $a_{2 k}$
and the terms of odd index by $a_{2 k+1} .$ Prove that if $a_{2 k} \rightarrow L$ and
$a_{2 k+1} \rightarrow L,$ then $a_{n} \rightarrow L$

3.2 problem 54 They give us matrices A and s there in by in s is in vertical. They wanted to show that the determinant of s inverse A s squared is equal to the determinative A quantity squared. So let's just start looking at this. What is the determinate off? So we've got s inverse A s square. So that is the determinant I have. So that's s inverse A s Times s in verse A s. That's what it means to square that in particular quantity. What you see here is this s times as in verse, that becomes the end Any matrix. So this is equal to the determinant of s in verse and then you've got a hey s Well, we know that s is in vertebral So it's determinate is not zero. So let's just let will say s one is equal to the determinant of s So what this becomes this is the terminate of s in verse, times the determinant of a times A determinate of a from the determinant of s if s one is the determinant of s then this just becomes one over s one determinate of a determinative a times s one. So this is just the terminate of a times the determinant of a which is the determinant of a squared, and that's what we're out to prove.


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