Consider the matrix AV==-2Ga211 2 5-α-αW =0LO(1¹).where a ER, andZ =(8).Then,a) the linear system Ax = v has only one solution for a 0.b) the linear system Ax: = z has an infinite number of solutions for any value of a.c) the linear system Ax = w has no solutions for a == 0.d) the linear system Ax = v has an infinite number of solutions for a = = 0.e) none of the other answers.

Answered: Image /qna-images/answer/b3dc8a9b-757d-4818-b654-b8be9fdce662.jpg

Answered: Consider the matrix A = -2 1 1 2 α -α…

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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Do 2b)
2. Consider the system Ax = b with 1 -3 -5 10 -2-48 -3 10 15 A ,b= 50 12 (a) Write down each of the elementary matrices that reduce A to an upper triangular matrix U. (b) Write down the system Ux = c which is equivalent to Ax = b. (c) Solve the system Ux = c for x. No image
-x + y + 2z = 1 2x + 3y + z = -2 5x + 4y + 2z = 4 a) Find the RREF for the augmented array associated with this system, b) Find the solution to this system. c) What is the rank of the coefficient matrix? d) Is the coefficient matrix invertible?
Find the LU factorization of A = and then use it to solve the system -4 -3 3 16 15 -11 A = x1 = x₂ = x3 = 8 -6 -8 || x1 x2 x3 = -4 -3 3 16 15 -11 8 -6 -8 -31 127 44 " such that the matrix L has ones along the diagonal,
2. A is a 4 x 5 matrix with four pivot positions. a) Does the equation Ax = 0 have a nontrivial solution? b) Does the equation Ax = b have at least one solution for every possible b?
4) Consider the system of linear equations: X1 + 5x2 + 3x3 = 4 X1 – X2 + 6x3 = 16 2x1 + x2 = 5 a) Write the system as Ax=b b) Solve the system using Gaussian Elimination with backward substitution. c) What is the determinant of A. d) Perform one step of the Gauss-Seidel Method on this system starting with initial guess 1 1
9) 1 of the matrix B x A? Let A = 1 0 -2 1 and B = 2 -1 1 1 :) 1 What is the entry on the row 2 and column
8. Solve the linear system Ax-b by x₁ + x₂-3x₂ = -1 -x₁ + 2x₂ = 1 x₁ - x₂ + x₂ = 2 a) finding the LU-factorization of the coefficient matrix A b) Solving the lower triangular system Ly-b. c) solving the upper triangular system Ux-y.
The RREF of the augmented matrix corresponding to the system of linear equations, Ax =b , is 1 2 -1 5 4 0 0 1 3 0 0 1 -7 0 0 a) b) Hence, write the solution of the system in vector form. Give a basis for the solution set of the corresponding homogeneous system, Ax = 0. Find: rank(A), nullity (A), rank(A"), and nullity (A"). c)
Find the solutions (x1, x2, x3) for the linear system with various parameters (a, b). 2x13x2+ ax3 = 1 2x13x2+2x3 = b 4x13x2+2x3 = 4 (a) a = 4, Vb Є R (b) a = 2,b=1 (c) a=2, Vb ERǝb 1 Perform row reduction starting with the augmented matrix and ending with reduced row echelon form. Show each row reduction step. If the system has no solutions, explain why. If the system is consistent, find all solu- tions. In the case of infinitely many solutions, use parameters.
The percentage of female high school graduates who enrolled in college is given in the table below. Year 1970 1980 1990 2000 2010 College Enrollment Percentages for Females 25.5 30.3 38.3 45.6 50.5 Let a represent time (in years) since 1970, and let y represent the corresponding percentage of female high school graduates who enrolled in college. Find the cubic regression model y = F(x) = ax³ + bx² + cx + d, = where a is rounded to 6 decimal places, b is rounded to 4 decimal places, c is rounded to 3 decimal places, and d is rounded to 1 decimal place.

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