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

Question

-x +3y-z =-4
2x +6z=14
-2x - y+ z=10

Answer 1

The system of linear equations are .

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.

Perform the operations on so first column has leading .

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

Perform the operations on so second column has leading .

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

Perform the operations on so third column has leading .

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

Substitute the value of in and solve for y.

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The value of are substitute in and solve for x.

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The solution .