Question

Solve the following systems of equations using matrix method. 

x - y – 2z = 3; 

x + y = 1; 

x + z = - 6.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

x - y - 2z = 3 

x + y = 1 

x + z = - 6 

Converting the following equations in matrix form, 

AX = B

R₂ – R₁ 

R₃ – R₁

Again converting into equations we get 

x + y - 2z = 3 

2y + 2z = - 2 

4z = - 16 

z = - 4 

2y – 8 = - 2 

2y = - 2 + 8 

2y = 6 

y = 3 

x - 3 + 8 = 3 

x = - 2 

∴ x = - 2 , y = 3 , z = - 4