Question

Solve the following systems of equations using matrix method. 

x + 2y + z = 4; 

- x + y + z = 0; 

x - 3y + z = 4

Answer 1

To find: - x , y , z 

Given set of lines are : - 

x + 2y + z = 4 

- x + y + z = 0 

x - 3y + z = 4 

Converting the following equations in matrix form, 

AX = B

R₂ + R₁ 

R₃ – R₁

Again converting into equations we get 

x + 2y + z = 4 

3y + 2z = 4 

- 5y = 0 

y = 0 

0 + 2z = 4 

z = 2 

x + 0 + 2 = 4 

x = 2 

∴ x = 2 , y = 0 , z = 2