6. [10 marks] Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of T. (a) How many vertices does BL(T) have? (b) How many edges does BL(T) have? Prove that your answers are correct.

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A: Since p∈P1​, it implies that p is a polynomial of degree at most one.Therefore, let p(x)=ax+b where…

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A: Step 1:1. Understand the Problem and Basis Vectors Step 2: Construct the Projection Matrix PPP Step…

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A: From the question, we have the following values:A = 61B = 554C = 7234D = 0.61E = 5.54Weight of each…

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Q: A 0 -0- 2 Example: -x°=-Ax find EC, ES, ε" and E draw phase portmail.

A: Phase Portrait  1. Eigenvalues of A:A=⎣⎢⎡​010​−100​002​⎦⎥⎤​To find the eigenvalues, solve the…

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A: The five points of the first cycle are:(−0.42403, 0),(−1.14677, 0),(0, −3),(4π​, −7)and(−4π​, 1)

Q: -4 m 1.0 1,0 0 Let f(x) = {º (3 - x) • - - -3 for 0 < x < 1, for 1 < x < 3. Compute the Fourier sine…

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Q: 33. Page 49 The problem concerning solving a system of linear equations can be found on page 49.…

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Q: Consider G = {zЄ C: z° = 1} Show that G is a cyclic group by writing a generator of G.

A: We are given the set (G={z∈C:z6=1}), which represents the sixth roots of unity. Let's show that ( G…

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A: For the scatterplot and regression models, I used desmos.comStep 1: Input the data in table format.…

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Q: Refer to page 18 for solving a second-order linear non-homogeneous differential equation.…

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A: Reduced Row Echelon Form: A matrix is said to be in reduced row echelon form if satisfies the…

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A: Step 1: Step 2: Step 3: Step 4: Step 5: Step 1: Step 2: Step 3: Step 4:

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Q: Го 2 1 -1 0 0 Show that A 3 5 3 and B = 0 -3 2 are similar matrices by finding an invertible matrix…

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Q: Refer to page 81 for a proof involving the uniqueness of solutions for a given ordinary differential…

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A: Step 1: Given equation is f(x)=−(x−3)(x+2)(x+4)2. We need to determine the degree, leading…

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A: Let's go step-by-step to thoroughly understand the system and its classification: Step 1:…

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Q: Let U, V and W be vector spaces. Let S : U → V and T : V → W be linear transformations. Define R: U…

A: a) Problem 1: Show that R is a linear transformation.To prove that R is a linear transformation, we…

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A: Two matrices can be added if they are of the same size. The size of a matrix refers to its…

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A: Here's how to find the orthogonal decomposition of v with respect to the subspace W: 1. Find an…

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A: Step 1: Set Up Fairness Equations Step 2: Solve for x Using p1​ ​

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Q: Refer to page 89 in the shared document for a basic algebra problem. Solve the equation for the…

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Q: /show that Sin z=0 where k is an integer. iff z= k*

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Q: A project schedule has the following characteristics as shown in Table Activity Name Time Activity…

A: Step 1: Construct PERT NetworkNodes represent events, and directed edges represent activities.Each…

Q: 3. Let {X} be an autoregressive process of order one, usually written as AR(1). (a) Write down an…

A: a)b)c)d)

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Q: (3) Let G be a group and let gЄ G. Prove that the function f : G→ G given by f(x) = gx is bijective…

A: We prove that the function f: G→ G given by f(x) = gx, where g ∈ G, is bijective by showing it is…

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Q: 1. Please solve Advanced Mathematics Assignment Refer to page 10 inside the provided drive. All…

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A: Solution:Step 1: Review of the integral and singularityThe integral isz+11​,which has a singularity…

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A: Detailed explanation: The Adjacency Matrix is as follows:…

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A: Step 1: We need to find the time when the ball reaches a height of 26 m  We can set the equation…

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A: Detailed explanation: (a) Are these species predator-prey or competing?The system of equations…

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