Solve the system of equations using the methods of matrix row reduction.

Question

2x+y+2z=-4 

4x+3y-z=1 

5x-4y+3z=-34 

What is the solution?

Answer 1

System of equations are and .

Row-reduction method :

A linear system is represented as an augmented matrix.

If  are the system of equations then the augmented matrix is .

Reduce the augmented matrix into row echelon form, by using elementary row operations.

Row echelon form of linear system of three variable is .

The solutions of the system of equation are  and . 

Consider augmented matrix .

Apply elementary row operations to the above matrix.

The above matrix is in the form of Row echelon form.

Therefore, ,  and .

Solution of the linear system is ,  and .