Please help!! Solve the following using matrices.

Question

x-3y+z=2
4x-12y+4z=8
-2x+6y-2z=-4
I am taking a class on-line and am not getting the one on one I need for these problems.
thank you in advance

Answer 1

Gauss - Jordan Elimination :

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.

.

are represent the first row, second row and third row respectively.

The first column has already leading 1 in upper left corner.

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

Now the matrix is in reduced row - echelon form, and converting back to a system of linear equations is .

 

The resultant equations 2 and 3 have no variables. The statement is true, so the system of equations has infinitely many solutions.