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Solve using Gauss-Jordan Elimination Method










































Solve System of Equations with 3 variables

-3x + 6y - 9z = 3
x - y - 2z = 0
5x + 5y - 7z = 63

Solve the system of linear equations using the Gauss-Jordan Method. I can start it but not sure where to go from the beginning.

Comments for Solve using Gauss-Jordan Elimination Method

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Mar 07, 2013
Gaussian Elimination
by: Staff


Answer



Part I

The system of equations in your problem statement is:

 system of 3 equations with 3 unknowns:  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63






The augmented matrix for this system of equations is:

augmented maxtrix for:  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63





The row operations used by the Gaussian elimination method are:

gauss-jordan elimination method - 01 - row-operation:  divide row 1 by -3;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63





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Mar 07, 2013
Gaussian Elimination
by: Staff


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Part II

gauss-jordan elimination method - 02 - row-operation:  add (-1)*row 1 to row 2;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63




 gauss-jordan elimination method - 03 - row-operation:  add (-5)*row 1 to row 3;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63




gauss-jordan elimination method - 04 - row-operation:  add (-15)*row 2 to row 3;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63






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Mar 07, 2013
Gaussian Elimination
by: Staff


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Part III

gauss-jordan elimination method - 05 - row-operation:  divide row 3 by 53;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63




gauss-jordan elimination method - 06 - row-operation:  add 5*row 3 to row 2;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63




 gauss-jordan elimination method - 07 - row-operation:  add (-3)*row 3 to row 1;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63






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Mar 07, 2013
Gaussian Elimination
by: Staff


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Part IV

gauss-jordan elimination method - 08 - row-operation:  add 2*row 2 to row 1;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63




Convert the final matrix back into equation form:

convert final matrix into equation form;  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63





The three equations have a diagonal of 1's. The the answers are all in the last column.


Final Answer :

guass-jordan elimination method - final solution to:  -3x + 6y - 9z = 3, x - y - 2z = 0, 5x + 5y - 7z = 63







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Mar 07, 2013
Gaussian Elimination
by: Staff


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Part V




Check the answer by substituting the numerical values of x, y and z into the original equations:

-3x + 6y - 9z = 3

-3*8 + 6*6 -9*1 = 3

-24 + 36 - 9 = 3

3 = 3, correct


x - y - 2z = 0

8 - 6 - 2*1 = 0

2 - 2 = 0

0 = 0, correct


5x + 5y - 7z = 63

5*8 + 5*6 - 7*1 = 63

40 + 30 - 7 = 63

63 = 63, correct



Since the numerical values of x, y, and z work in all three of the original equations, the solutions are correct.






Thanks for writing.

Staff
www.solving-math-problems.com



Dec 12, 2016
solution NEW
by: Anonymous

for those who want step by step answer for any linear system get
Gauss calculator app for android
from google play :)
https://goo.gl/wFJ8gr
thank me later ;)

Apr 30, 2017
help solve NEW
by: Anonymous

The Collin freight company has an order for three product to be delivered to a destination. Product I requires 10 cubic feet, weighs 10 pounds and has a value of $100. Product II requires 8 cubic feet, weighs 20 pounds, and has a value of $20. Product III requires 20 cubic feet, weighs 40 pounds, and has a value of $200. If the carrier can carry 6,000 cubic feet, 11,000 pounds, and is insured for $ 36,900, how many of each product can be carried. 1.Identify the variables of the problem using x, y, and z.

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