A=-ΤΟ 1000 0 2000030 00(3)Consider the following linear system: Axb, where A is given by (3), as in Problem 4, and vectorb = [0, 0, 0, 2023]T. Since matrix A is singular, there are infinitely many least squares solutions. Find theleast squares solution x* with the minimal Euclidean norm.

The given matrix is and .We need to find the least square solution of the system with minimal…

Answered: A = 0 1 00 0020 00 03 000 0 = (3)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. If the equation Gx = y has more than one solution for some y & R", can the columns of G span R"? (you can use Invertible Matrix Theorem) Note. If the equation Hx = c is inconsistent for some c = R", what can you say about the equation? (you do not need to submit).
1. In each part of this question, you have been given a system of equations and the corresponding matrix taken to RREF. Write the general solution as a vector equation. • List the basic solutions. a. b. (x₁ - x₂ + 2x4 = 0 [1 -X₁ + x₂ + 3x3 - 11x4 0 2x₁ - 2x₂ + 4x4 0 0 -4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo - = 0 " -1 0 2 01 0 1 -3 0 0 0 0 0 0 00 (3w+9y15z = 0 1 0 -14w + 33x - 75y - 62z = 0 0 1 -5w+ 14x - 29y - 31z = 0 0 0 (52w 164x + 320y + 396z = 0 Lo 0 3 -1 -4 0 0
2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?
5x1 + 6x2 + 11x3 + 7x4 6x5 5 4. Membership in a Span: For every item: (i) apply the Modified Gauss-Jordan Algorith to determine if b is in Span(S); (ii) write the solution vector i if there are solutions to ti corresponding augmented matrix; (iii) express S in the simplest possible way, and check directly that your answer is correct. as a linear combination of the vectors а. Б - (-4, 2, -3); S - {{7,4, -6), (-5, -2, 3)} b. b = (-4, 2,–4); S = {(7,4,–6), (-5,–2, 3)} %3| b = (9, 7,-8, 2); S = {(5,-3, 2, 6), (-2,–3, 5, 8), (–5, 4,–2,–3)} d. b = (-10, 13,–4, 9); S = {(5,-3, 2, 6), (-5, 4,–2,–3), (-5, 7,–2, 6)} Б - (13, 14,-18,-11); S = {(5,-3, 2, 6), (–2,–3, 5, 8), (–5, 4,–2,–3), (11, 10,–13,-6)} b = (8,–9,–8, 15,-3), S = {(6,0,4, 3, 2), (3, 2, 7, 1,–2), (2, 1, 2, –1, 3)} b = (-4,–1, 4, 7,-9), S = {(3, 2, 7, 1,–2), (2, 1, 2,–1, 1), (1, 0,–3,–3, 4)} h. Б - (-3,6, -1,-9, 4), S = {(6,0,–1, 3, 2), (3, 2,–3, 1,–2), (0,–4, 5, 1, 6), (3,–2, 1, 3, 3)} с. %3D е. f. g.
Please solve all the parts
1. 0 2 4 1 -1 10 0 0 1 1 The reduced row echelon form of the augmented matrix of a linear system is given above. Describe the solution set of this linear system in parametric vector form.

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A = 0 1 00 0020 00 03 000 0 = (3) Consider the following linear system: Ax b, where A is given by (3), as in Problem 4, and vector 6 = [0, 0, 0, 2023] T. Since matrix A is singular, there are infinitely many least squares solutions. Find the east squares solution x* with the minimal Euclidean norm.