To find: - x , y , z

Given set of lines are : -

2x - 3y + 5z = 11;

3x + 2y - 4z = - 5;

x + y – 2z = - 3.

Converting the following equations in matrix form,

AX = B

2R₂ – 3R₁

2R₃ –R₁

13R₃ - 5R₂

Again converting into equations we get

2x – 3y + 5z = 11

13y - 23 z = - 43

- 2z = - 6

Z = 3

13y - 23×3 = - 43

13y = - 43 + 69

13y = 26

Y = 2

2x – 3×2 + 5×3 = 11

2x = 11 + 6 - 15

X = 1

∴