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The use of Matrices and Gaussian elimination with back-substituion to solve the system of the linear equation.

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-x +3y-z =-4
2x +6z=14
-2x - y+ z=10
asked Mar 17, 2014 in ALGEBRA 2 by skylar Apprentice

1 Answer

+1 vote
 
Best answer

The system of linear equations are image.

The system of linear equations can be written as the form of augmented matrix or [A : B ], where A is coefficient matrix and B is constant matrix.

image

Perform the operations on image so first column has leading image.

image

Perform the operations on image so first column has zeros below its leading 1.

image

Perform the operations on image so second column has leading image.

image

Perform the operations on image so second column has  zeros below its leading 1.

image

Perform the operations on image so third column has leading image.

image

Now the matrix is in reduced row-echelon form, and corresponding system is image.

Substitute the value of image in image and solve for y.

image

image.

The value of image are substitute in image and solve for x.

image

image

image.

The solution image.

answered Mar 28, 2014 by steve Scholar
selected May 13, 2014 by skylar

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