6. Use the Gaussian Elimanation to write the determine conditions on the c's, if any, in order to guarantee that the linear system is consistent. - x2+3x3+ 2x4 = c1 -2x1+ x2 + 5x3 + x4 = C2 3x1- 2x2- 2x3 +x4 = - C3 - 4x1+3x2- x3 – 3x4 C4 %3D |

6. Use the Gaussian Elimanation to write the determine conditions on the c's, if any, in order to guarantee that the linear system is consistent. - x2+3x3+ 2x4 = c1 -2x1+ x2 + 5x3 + x4 = C2 3x1- 2x2- 2x3 +x4 = - C3 - 4x1+3x2- x3 – 3x4 C4 %3D |

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

answer it asap and correctly
4. Use the SOR method with w = 1.2 to solve the linear systems 4x1 + x2 + X3+ Xs = 6, -x – 3x2 + x3 + x4 = 6, 2x, + x2 + 5xz – X4 - x5 = 6, -XI - x2 - X3 + 4x4 = 6, 2x2 - x3 + xX4 +4x3 = 6. with a tolerance TOL = 10-3 in the loo norm.
5. Find an equation involving g,h, and k that makes this augment matrix corre- spond to a consistent linear system: 1 -4 3 -5 h -2 5 -9 k
12. Let A = 1 1 12 1 3 -[]. and b = (1) Use the Existence and Uniqueness Theorem to show Ax = b is an inconsistent linear system. (2) What is the normal equation? (3) Find a least-squares solution to the inconsistent system Ax = b.
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.
Select T if the statement is true (in all cases), or select F if false (for at least one example).
ii. Define Cramer's rule and use it to solve the following system of linear equations. 0.4x- 0.3y = 1 0.3x + 0.4y = 2 %3D
4. Use Gaussian elimination with backward substitution to solve the following linear system: 2x1 + x2 – x3 = 5, x1 + x2 – 3x3 = -9, -x1 + x2 + 2x3 = 9;
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.
5. Formulate Cramer's rule, and, if possible, solve the following linear system using it: X1 + 2x2 X3 -3 X1 X3 -1 3x1 X2 + 2x3 13