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# Solved: Solve the systems in Exercises 11–14.x1 – 5x2 + ISBN: 9780321982384 49

## Solution for problem 12E Chapter 1.1

Linear Algebra and Its Applications | 5th Edition

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Problem 12E

PROBLEM 12E

Solve the systems in Exercises 11–14.

 x1 – 5x2 + 4x3 = –3 2x1 – 7x2 + 3x3 = –2 – 2x1 + x2 + 7x3 = –1
Step-by-Step Solution:

Solution 12E :

Step 1 :we given the system of equations

x1 -5x2 +4x3 = -3

2x1 -7x2+ 3x3 = -2

-2x1 +x2 +7x3 = -1

The system of equation can be return in  the form      AX = B

Where A is the coefficient matrix , X is the column matrix of unknowns and B is the column matrix of constants.

Step 2 : we have to find the solution of the system

The solution of a system of linear equations can be of three types. They are:-

(i) One solution (ii) Infinite solution and (iii) No solution

Let the augmented matrix of A and B is [A :B],  the solution is depend on the rank of augmented matrix and rank of A i.e. and number of unknowns (n)

So we get (i) One solution - if = = (n)

(ii) Infinite solution - if = <  (n)

(iii) No solution - if   Step 3 of 3

##### ISBN: 9780321982384

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