Matrices question help please!?

Question

solve the system using matrices (row operations) 
-2x+5y+3z = 10 
-5x- 2y-4z = 16 
-3x-5y+4z = -21 

x = ? 
y= ? 
z=? 

THANK YOU!

Answer 1

Step 1:

The system of equations are  

Write the equations into matrix form ,

Write the equations into matrix form , where is coefficient matrix,

is variable matrix and is constant matrix.

Solve the equations in Gauss-Jordan method.

The augmented matrix is .

Step 2:

The augmented matrix is

Apply elementary row operations to obtain a reduce the row-echelon form.

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

Solution :

The solutions of the augmented matrix are and .