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 |

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 60EQ

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Question

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.
x1 – x2+ 3x3 + 2x4 = cj
- 2x1 + x2+ 5x3 + x4 = C2
3x1- 2x2- 2x3 + x4 = C3
-4x1+3x2– x3 – 3x4 =
= C1
– C4
-
77°F
e Type here to search

Expert Solution

Step 1: Given.

Given: A system

$x_{1} - x_{2} + 3 x_{3} + 2 x_{4} = c_{1} - 2 x_{1} + x_{2} + 5 x_{3} + x_{4} = c_{2} 3 x_{1} - 2 x_{2} - 2 x_{3} + x_{4} = - c_{3} - 4 x_{1} + 3 x_{2} - x_{3} - 3 x_{4} = - c_{4}$

To find: Condition on $c$ 's so that the given system is consistent.

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