Q30 of 98 Page 310

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

2x + y - z = 1;


x – y + z = 2;


3x + y – 2z = - 1.



To find: - x , y , z


Given set of lines are : -


2x + y - z = 1


x - y + z = 2


3x + y - 2z = - 1


Converting the following equations in matrix form,


AX = B



2R2 – R1


2R3 – 3R1



3R3 - R2



Again converting into equations we get


2x + y – z = 1


- 3y + 3z = 3


- 6z = - 18


Z = 3


- 3y + 3×3 = 3


- 3y = 3 - 9


- 3y = - 6


Y = 2


2x + 2 - 3 = 1


2x = 1 + 1


X = 1


∴ x = 1 , y = 2 , z = 3


More from this chapter

All 98 →
28

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

3x - 4y + 2z = - 1;


2x + 3y + 5z = 7;


X + z = 2.


 29

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

X + y - z = 1;


3x + y – 2z = 3;


X – y – z = - 1.


 31

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

X + 2y + z = 4;


- x + y + z = 0;


x - 3y + z = 4.


 32

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

x - y – 2z = 3;


x + y = 1;


x + z = - 6.