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a) Show that the system of simultaneous linear equation in

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 24E Chapter 2.6

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 24E

Problem 24E

a) Show that the system of simultaneous linear equation

 

in the variables x1,x2,…, xn can be expressed as

AX = B, where A = [aij], X is an n × 1 matrix with xi the entry in its ith row, and B is an n × 1 matrix with bi the entry in its ith row.

 b) Show that if the matrix A = [aij] is invertible (as defined in the preamble to Exercise 18), then the solution of the system in part (a) can be found using the equation X = A-1 B.

Step-by-Step Solution:

Solution:

Step 1


In this problem we need to show that a
system of simultaneous linear equations




                                                   

In variables can be written as. We also need to show that the solution of the system of linear equations can be found using the equation  if the matrix  is invertible.

Step 2 of 3

Chapter 2.6, Problem 24E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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a) Show that the system of simultaneous linear equation in