Answered: 1.2.15. (!) Let W be a closed walk of… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 47E

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1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle.
Prove that some edge of W repeats immediately (once in each direction).

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3. [10 marks] Let Go = (V,E) and G₁ = (V,E₁) be two graphs on the same set of vertices. Let (V, EU E1), so that (u, v) is an edge of H if and only if (u, v) is an edge of Go or of G1 (or of both). H = (a) Show that if Go and G₁ are both Eulerian and En E₁ = Ø (i.e., Go and G₁ have no edges in common), then H is also Eulerian. (b) Give an example where Go and G₁ are both Eulerian, but H is not Eulerian.
6. The covariance between X and Y is calculated and recorded as SXY (and sxy is a negative number). A linear transformation is performed on X. The linearly transformed variable is called W, where W; = 5 + Xi. The covariance between W and Y is calculated and recorded as sWY. Which statement is correct? A) В) In this example, swy would be less than sxY. In this example, swY Would be equal to sxY. In this example, swy would be greater than SXXY. 7. The covariance between X and Y is calculated and recorded as sxy (and sxy is a positive number). A linear transformation is performed on X. The linearly transformed variable is called W, where W; = (4)X;. The covariance between W and Y is calculated and recorded as sWY. Which statement is correct? In this example, sxY would be less than swy. In this example, sxY Would be equal to swy. In this example, sxY would be greater than sWY. A) B) 8. The correlation between X and Y is calculated and recorded as rxY (and rxy is positive). A linear…
2,4 Let f (x, y) : if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8)
[:] Suppose that T is a linear transformation from ³ into ² such that 3 -[-2]. (₂) - [8].a T -[2], and T(3) = [1] The columns of k T(e₁) O *1 Tx2 = 2x1 x3 *1 TX2 002 1 0 0 0 Tx2 = *3 3x1-2x2] Tx2 = 2x1 001 Find a formula for the image of an arbitrary x= x2 in ³. 4x2 + x3 1 0 are e₁ 3x1 + 2x2 - 4x3 -2x1 + x3 3x1-2x1 2x1 3x1 + 2x2-4x3 -2x1 wwww + X3 x3 0 e2 ез 0 akan wwwwww.
23. Suppose R* = Span {v1, ..., V4}. Explain why {v1,..., V4} is a basis for R4.
1.6 (Equality in Cauchy-Schwarz inequality). Prove that |(x, y)| = ||x|| - ||y|| if and only if one of the vectors is a multiple of the other. Hint: Analyze the proof of the Cauchy-Schwarz inequality.
8.6 This exercise provides an alternative to Theorem 8.2 for factoring an r-cycle into transpositions. Prove that (X1, X2, X3, ..., x,) = (x1, x2) • (x2, x3) • (X3, x4) o • (x~2, X-1) • (X-1, x,). O ... O
8. Find the max and min of |(z + 1)²e¯²| in the disk |z| ≤ 1.
Let T be a linear transformation from M2,2 into M2,2 such that ([:))-[2] ([:))-[:] [:))-[:] [:))-[1] Find ([-1³). 3 12 7 -1 3 ↓ 1 X Need Help? Read It Watch It MY N
2. Is there a linear map from R³ to R³ such that T(1,3,0) = (0,0,0) and T(-2,0,0) = (0,0,0) and T(3, 7, 1) = (3, 2, -3)?
6. Let T: R³ → R² be given by 74-7 8-6.5.) = T Show that I is a linear transformation by confirming the two conditions of the definition.

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