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# a) Show that the system of simultaneous linear equation in ISBN: 9780073383095 37

## Solution for problem 24E Chapter 2.6

Discrete Mathematics and Its Applications | 7th Edition

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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</p>

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</p>

Consider a matrix A such that and a matrix X such that .

The multiplication of the matrices A and X is possible since number of columns of A are equal to the number of rows of B so we write  If given simultaneous system of linear equations are        Then we can write  Hence it is shown that the given system of linear equations can be written in the form .

Step 3 of 3

##### ISBN: 9780073383095

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