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Solve each system in three variables using Gaussian elimination.

0 votes
State whether each system is independent, dependent, or inconsistent.
x - y + z = 2
-x + y + z = 4
-x + z = 2
asked Mar 17, 2014 in ALGEBRA 2 by payton Apprentice

1 Answer

0 votes

Gaussian Elimination:

The linear equations are x  - y  + z  = 2, - x  + + = 4 and - + z  = 2.

Write the equations into matrix form AX = D .

is coefficient matrix , is variable matrix and is Constant matrix.

image

The augmented matrix is [AD ]

image

image  are represents first row ,second row and third row .

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image

image

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Solution : x  = 1, = 2, z  = 3.

The system of equations has exactly one solution, so the system is consistent and independent.

answered Sep 4, 2014 by david Expert

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