Solve each of the following systems of equations using matrix method.

6X - 9y – 20z = - 4;


4x – 15y + 10z = - 1;


2x - 3y - 5z = - 1.



To find: - x , y , z


Given set of lines are : -


6x - 9y - 20z = - 4


4x – 15y + 10z = - 1


2x - 3y - 5z = - 1


Converting the following equations in matrix form,


AX = B



3R2 – 2R1


3R3 – R1



Again converting into equations, we get


6x - 9y - 20 z = - 4


- 27y + 70z = 5


5z = 1


Z =


- 27y + 70 = 5


- 27y = 5 – 14


- 27y = - 9


Y =


6x – 9× - 20 × = - 4


6x = - 4 + 3 + 4


X =



1