Explanation Given: The system of equations x − y + z = 5 , x + y + 3 z = 11 , − x + 2 y − z = − 5 . Formula Used: The augmented matrix [ A | I ] is equivalent to the augmented matrix [ I | A − 1 ] . The solution to the matrix equation A [ x y z ] = B is gives by: x = D x D y = D y D z = D z D Here D x is the determinant of the matrix formed by replacing the first column in A by the column matrix B , D y is the determinant of the matrix formed by replacing the second column in A by the column matrix B and D z is the determinant of the matrix formed by replacing the third column in A by the column matrix B and D is the determinant of matrix A . Calculation: Consider the system of equations: x − y + z = 5 x + y + 3 z = 11 − x + 2 y − z = − 5 The augmented matrix for the system would be: [ 1 − 1 1 5 1 1 3 11 − 1 2 − 1 − 5 ] Now perform the following row operations to obtain the solution. − R 1 + R 2 → R 2 , R 1 + R 3 → R 3 give, [ 1 − 1 1 5 0 2 2 6 0 1 0 0 ] 1 2 R 2 → R 2 gives, [ 1 − 1 1 5 0 1 1 3 0 1 0 0 ] R 2 + R 1 → R 1 , − R 2 + R 3 → R 3 gives, [ 1 0 2 8 0 1 1 3 0 0 − 1 − 3 ] − R 3 → R 3 gives, [ 1 0 2 8 0 1 1 3 0 0 1 3 ] − 2 R 3 + R 1 → R 1 , − R 3 + R 2 → R 2 gives, [ 1 0 2 2 0 1 1 0 0 0 1 3 ] This gives the solution to the system of equations as x = 2 , y = 0 , z = 3 . This can be rewritten as the following matrix equation: [ 1 − 1 1 1 1 3 − 1 2 − 1 ] [ x y z ] = [ 5 11 − 5 ] A X = b Use the Gaussian elimination to obtain the inverse of A . The augmented matrix would be: [ 1 − 1 1 1 0 0 1 1 3 0 1 0 − 1 2 − 1 0 0 1 ] Now perform the following row operations: − R 1 + R 2 → R 2 , R 1 + R 3 → R 3 gives, [ 1 − 1 1 1 0 0 0 2 2 − 1 1 0 0 1 0 1 0 1 ] 1 2 R 2 → R 2 gives, [ 1 − 1 1 1 0 0 0 1 1 − 0.5 0

College Algebra Plus New Mymathlab With Pearson Etext Access Card

6th Edition

ISBN: 9780321919748

Author: Mark Dugopolski

Publisher: PEARSON

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Chapter 6, Problem 38RE

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To calculate: The Solution of the system of equations

x−y+z=5,x+y+3z=11,−x+2y−z=−5

using Gaussian elimination.

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Chapter 6, Problem 37RE

Chapter 6, Problem 39RE

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Chapter 6 Solutions

College Algebra Plus New Mymathlab With Pearson Etext Access Card

Ch. 6.1 - True or False? Explain. The augmented matrix for a...Ch. 6.1 - Prob. 2FT Ch. 6.1 - Prob. 3FT Ch. 6.1 - Prob. 4FT Ch. 6.1 - Prob. 5FT Ch. 6.1 - Prob. 6FT Ch. 6.1 - Prob. 7FT Ch. 6.1 - Prob. 8FT Ch. 6.1 - True or False? Explain. The system corresponding...Ch. 6.1 - Prob. 10FT

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The Solution of the system of equations x − y + z = 5 , x + y + 3 z = 11 , − x + 2 y − z = − 5 using Gaussian elimination.

Solution Summary: The author calculates the solution of the system of equations x=2,y=0,z=3 using Gaussian elimination.

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To calculate: The Solution of the system of equations

x−y+z=5,x+y+3z=11,−x+2y−z=−5

using Gaussian elimination.

Want to see the full answer?

Chapter 6 Solutions

The Solution of the system of equations x − y + z = 5 , x + y + 3 z = 11 , − x + 2 y − z = − 5 using Gaussian elimination.

Solution Summary: The author calculates the solution of the system of equations x=2,y=0,z=3 using Gaussian elimination.

Concept explainers

Videos

To calculate: The Solution of the system of equations x−y+z=5,x+y+3z=11,−x+2y−z=−5 using Gaussian elimination.

Want to see the full answer?

Chapter 6 Solutions

To calculate: The Solution of the system of equations

x−y+z=5,x+y+3z=11,−x+2y−z=−5

using Gaussian elimination.