A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0,...

A non-uniform b-spline curve knot vector is given as (-1, -1, -1, -1/2, 0, 0, 0, 1, 1, 1, 3/2, 2, 2, 3, 3, 3, 3). Show the equation diagrammatically and sketch the curve with their respective control polygons if the curve is cubic (degree 3, order 4).

Expert Solution

Colby Messinger answered 2 years ago

1. Vector u =< 0,−1,3 > is given. Find a non zero vector v which is...

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Let a and b be non-parallel vectors (algebraically a1b2 −a2b1 /= 0). For a vector c...

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Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1...

Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1 ≠ ?2 and ?1, ?2 ≠ 0, A) Find necessary and sufficient conditions on a, b, and c such that A is diagonalizable. B) Find a matrix, C, such that C-1 A C = D, where D is diagonal. C) Demonstrate this with ?1 = 2, ?2 = 5, and a, b, and c chosen by you, satisfying your criteria from A).

2. Given A = | 2 1 0 1 2 0 1 1 1 |. (a)...

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Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector...

Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector space V and k ∈ R, k⃗0 = ⃗0. Justify for each of the eight steps why it is true. k⃗0+k⃗0=k(⃗0+⃗0) = k ⃗0 k⃗0 is in V and therefore −(k⃗0) is in V . It follows that (k⃗0 + k⃗0) + (−k⃗0) = (k⃗0) + (−k⃗0) and thus k⃗0 + (k⃗0 + (−k⃗0)) = (k⃗0) + (−k⃗0). We conclude that k⃗0 + ⃗0...

Given x = (-2, -1, 0, 1, 2) and response y = (0, 0, 1, 1,...

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1. Quadratic Lorenz Curve. Suppose the cumulative income distribution is given by x^2 , where 0...

1. Quadratic Lorenz Curve. Suppose the cumulative income distribution is given by x^2 , where 0 ≤ x ≤ 1, that represents the Lorenz curve of an economy. What is the Gini coefficient? Graph your results. For your information, the area under the Lorenz curve x^2 from 0 to 1 is 1/3 .

Problems 1-2 are based on the information given in the following table: Year A B 0...

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Let x3 be the following vector: x3 <- c(0, 1, 1, 2, 2, 2, 3, 3,...

Let x3 be the following vector: x3 <- c(0, 1, 1, 2, 2, 2, 3, 3, 4) Imagine what a histogram of x3 would look like. Assume that the histogram has a bin width of 1. How many bars will the histogram have? Where will they appear? How high will each be? When you are done, plot a histogram of x3 with bin width = 1, and see if you are right. I need code help R programming

Matrix: Ax b [2 1 0 0 0 | 100] [1 1 -1 0 -1 |...

Matrix: Ax b [2 1 0 0 0 | 100] [1 1 -1 0 -1 | 0] [-1 0 1 0 1 | 50] [0 -1 0 1 1 | 120] [0 1 1 -1 1 | 0] Problem 5 Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y. Solution: %code I have not Idea how to do this. Please HELP!

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