Question

Solve the following systems of equations using matrix method. 

2x + 3y + 3z = 5; 

x – 2y + z = - 4; 

3x – y – 2z = 3.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

2x + 3y + 3z = 5; 

x – 2y + z = - 4; 

3x – y – 2z = 3 

Converting the following equations in matrix form, 

ax = B

2R₂ – R₁ 

2R₃ – 3R₁

Again converting into equations we get 

2x + 3y + 3z = 5 

- 7y - z = - 13 

80 y = 160 

y = 2 

- 7×2 - z = - 13 

z = - 1 

2x + 3×2 + 3× - 1 = 5 

2x = 5 - 6 + 3

x = 1

∴ x = 1, y = 2, z = -1