Question

Solve the following systems of equations using matrix method. 

2x - 3y + 5z = 16; 

3x + 2y – 4z = - 4 

x + y – 2z = - 3.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

2x - 3y + 5z = 16; 

3x + 2y – 4z = - 4 

x + y – 2z = - 3 

Converting the following equations in matrix form,

AX = B

2R₂ – 3R₁ 

2R₃ – R₁

Again converting into equations, we get 

2x - 3y + 5z = 16 

13y - 23z = - 56 

- 2z = - 6 

Z = 3 

13y – 23 × 3 = - 56 

13y = - 56 + 69 

Y = 1 

2x - 3×1 + 5 × 3 = 16 

2x = 16 + 3 - 15 

2x = 4

x = 2

∴ x = 2, y = 1,z = 3