Consider the following system of linear equation 2x1 + 3x2 + 4x3 + x4 = 14 4x1 + 1x2 + 1x3 + 5x4 1x1 + 2x2 + 1x3 + 6x4 = = = 23 29 A) Find all basic solutions x= (x1, x2, x3, x4) obtained with B=[a2,a3,a4], i.e., the last three columns of matrix A of the linear system above. Then, FOR EACH BASIS, set XN (the non basic variable) something other than zero and obtain a solution which is NOT basic.
Consider the following system of linear equation 2x1 + 3x2 + 4x3 + x4 = 14 4x1 + 1x2 + 1x3 + 5x4 1x1 + 2x2 + 1x3 + 6x4 = = = 23 29 A) Find all basic solutions x= (x1, x2, x3, x4) obtained with B=[a2,a3,a4], i.e., the last three columns of matrix A of the linear system above. Then, FOR EACH BASIS, set XN (the non basic variable) something other than zero and obtain a solution which is NOT basic.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.7: Puzzle Problems
Problem 32P
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Question
![Consider the following system of linear equations.
2x1 + 3x2 + 4x3 + x4 14
4x1 + 1x2 + 1x3 + 5x4 = 23
1x₁ + 2x2 + 1x3 + 6x4 = 29
A) Find all basic solutions x= (x1, x2, x3, x4)
obtained with B=[a2,a3,a4], i.e., the last
three columns of matrix A of the linear
system above. Then, FOR EACH BASIS, set
XN (the non basic variable) something other
than zero and obtain a solution which is
NOT basic.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6b61458-362c-46a8-806a-8de7b1ef169c%2F9a23eaa5-6998-4123-9622-7e2fe9ab8275%2Ffilhk8a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following system of linear equations.
2x1 + 3x2 + 4x3 + x4 14
4x1 + 1x2 + 1x3 + 5x4 = 23
1x₁ + 2x2 + 1x3 + 6x4 = 29
A) Find all basic solutions x= (x1, x2, x3, x4)
obtained with B=[a2,a3,a4], i.e., the last
three columns of matrix A of the linear
system above. Then, FOR EACH BASIS, set
XN (the non basic variable) something other
than zero and obtain a solution which is
NOT basic.
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