Question

Solve the following systems of equations using matrix method. 

4x - 5y – 11z = 12; 

x – 3y + z = 1; 

2x + 3y – 7z = 2.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

4x - 5y - 11z = 12 

x – 3y + z = 1; 

2x + 3y – 7z = 2 

Converting the following equations in matrix form, 

ax = B

4R₂ – R₁ 

2R₃ – R₁

Again converting into equations we get 

4x – 5y - 11z = 12 

- 7y + 15z = - 8 

48 y = - 48 

y = - 1 

7 + 15z = - 8 

15z = - 15 

z = - 1 

4x + 5 + 11 = 12 

4x = 12 - 5 - 11 

4x = - 4

x = - 1

∴ x = - 1, y = - 1,  z = - 1