The eigenvalues of the coefficient matrix can be found by inspection orfactoring. Apply the eigenvalue method to find a general solution of the system.×₁ = 9x1 + 3x2 + 9x3, x2' = 3x₁ + 15×2 + 3x3, x3' = 9x1 + 3x2 +9x3What is the general solution in matrix form?x(t) =

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Answered: The eigenvalues of the coefficient…

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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The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply eigenvalue the system. the method to find a general solution of x₁ = 3x₁ + x₂ + 3x3 2 x ²₁ = x₁ + 5×₂ + x ₂ 3 x3 = 3x, +×ъ+ 3x3 What is the general solution in matrix form? x(t)=
Solve the equation Ax = b by using the LU factorization given for A. Also solve Ax = b by ordinary row reduction. A = y = 4 - 7 - 4 3 12 - 5 X = 4 3 -9 = 1 -1 00 10 3 - 4 1 Let Ly = b and Ux=y. Solve for x and y. 4 -7 -4 0 -4 - 1 0 0 - 1 Row reduce the augmented matrix [A b] and use it to find x. The reduced echelon form of [A b] is yielding x = 4 - 15 61
Find all solutions of the system (E) of linear equations -109z + 30y + 25z 6. 25z 7y + ly 6z 1 -3r 1z -4 Answer, step 1: The RREF of the augmented coefficient matrix of (E) is. B. Answer, step 1: (enter 1' for a true answer, and enter '0' for a false answer). The system (E) has infinitely many solutions The system (E) has exactly one solution The system (E) has no solutions Moreover, these solutions are: t + span{a, b} for nonparallel vectors a and b. For a vector that's not applicable enter -99' in each of its positions: if you mark a inapplicable, then b must be inapplicable also. t = b%3D Check
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A linear systje is defined by the following equatiosn, -x1 + x2 – x3 -1, 2.x1 + 6x2 – x3 6x1 + 5x2 + 3x3 3, 8. %3D From this linear system answer the following: (a) soning. Does the system have unique solution or infinite solution? Explain or show calculation with rea- (b) Find the augmented matrix for the linear system. (c) Solve the system using Gaussian elimination method.
2x + 2z = 12 x-z =4 Represent the system in matrix notation, and use Gaussian Elimination to solve for the unknowns
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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.
Let A be a 3x3 invertible matrix. The reduced row-echelon form of A is obtained by performing the following three elementary row operations in order: (1) First multiply row 1 by 1. (ii) Then add 3 times row 3 to row 2. (iii) Then finally interchange rows 3 and 2. Then what is det(A)? det(A) = 0

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The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. ×₁ = 9x1 + 3x2 + 9x3, x2' = 3x₁ + 15×2 + 3x3, x3' = 9x1 + 3x2 +9x3 What is the general solution in matrix form? x(t) =