2. Prove that |[0, 1]| = |(0, 1)|

Expert Solution

Colby Messinger answered 1 year ago

Prove that the 0/1 KNAPSACK problem is NP-Hard. (One way to prove this is to prove...

Prove that the 0/1 KNAPSACK problem is NP-Hard. (One way to prove this is to prove the decision version of 0/1 KNAPSACK problem is NP-Complete. In this problem, we use PARTITION problem as the source problem.) (a) Give the decision version of the O/1 KNAPSACK problem, and name it as DK. (b) Show that DK is NP-complete (by reducing PARTITION problem to DK). (c) Explain why showing DK, the decision version of the O/1 KNAPSACK problem, is NP-Complete is good...

0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.

0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4. A.)MEAN – B.)MEDIAN - C.)MODE - D.)STANDARD DEVIATION – E.)5 NUMBER SUMMARY – F.)BOX AND WHISKERS PLOT – G.) OUTLIERS-

0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.

0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4. A.)5 NUMBER SUMMARY – B.)BOX AND WHISKERS PLOT – C.) OUTLIERS-

Let A = [ 0 2 0 1 0 2 0 1 0 ]  . (a)...

Let A = [ 0 2 0 1 0 2 0 1 0 ]  . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly...

If p,p+2 are twin primes, prove 4((p−1)!+1)+p≡0 modp(p+2)

Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2,...

Consider the matrix A = [2, -1, 1, 2; 0, 2, 1, 1; 0, 0, 2, 2; 0, 0, 0, 1]. Find P, so that P^(-1) A P is in Jordan normal form.

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for...

2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all xin an interval ( a , b ), then f is constant on ( a , b ). b True or False. The product of two increasing functions is increasing. Clarify your answer. c Find the point on the graph of f ( x ) = 4 − x 2 that is closest to the point ( 0 , 1 ).

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly a diagonalizing...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly a diagonalizing...

A= 1 0 -7 7 0 1 0 0 2 -2 10 -7 2 -2 2...

A= 1 0 -7 7 0 1 0 0 2 -2 10 -7 2 -2 2 1 Diagonalize the matrix above. That is, find matrix D and a nonsingular matrix P such that A = PDP-1 . Use the representation to find the entries of An as a function of n.

Question

2. Prove that |[0, 1]| = |(0, 1)|

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