d₁ ≥ ≥ dn ≥ 0 with di even.di≤k(k − 1) + + min{k, di}vi=k+1T2.5: Let d1, d2,...,d be integers such that n - 1Prove the equivalence of the Erdos-Gallai conditions:for each k = 1, 2, ………, n and the Edge-Count Criterion: Σier di + Σjeл(n − 1 − d;) ≥ |I||J| forall I, JC [n] with In J = 0.

Answered: Image /qna-images/answer/56f6f13f-4f35-4015-b7b9-a27453221d48.jpg

Answered: d₁ ≥ ≥ dn ≥ 0 with di even. di≤k(k − 1)…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 42CR

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Prove the conjecture made in the previous exercise.
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Let X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently. 1. Compute P(−0.5X1 − X2 + 1.5X3 − 1.2X4 ≤ 5). 2. Compute P(|2.5X1 + 0.5X2 − 2.2X3 − 1.8X4 − 2| ≤ 4). 3. Compute P(2X1 − 1.2X2 ≤ 3.1X3 − 1.4X4 + 9).How can I compute these probabilities?
B₂ {(₂1 X12 X22 | Xij ≥ 0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, X11 + x21 (6) Let B₂ to be the set described in the screenshot attached Suppose Cij are real numbers such that C11C22 C12 + C21 > 0. Consider the following LPP: maximize: C11x11 + C12x12 + C21%21+ C22X22 subject to: (#11 #12) € B₂ X21 = 1.5, x12 + x22 = 2. (a) Write this problem in canonical form {x = (x11, 12, X21, X22) € R4 | Ax = b, x ≥ 0}. Hint: A should be a 3 x 4 matrix (after you eliminate one row which is linearly dependent on the others). (b) List all BFS. Which BFS x* has the maximum cost for this LPP? 2.5}. For the maximizer x*, show that for all basic directions D₁ at x* the reduced cost Cj = c² Dj ≤ 0.
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