To find: - x , y , z

Given set of lines are : -

x + y + z = 1;

x – 2y + 3z = 2;

5x – 3y + z = 3.

Converting the following equations in matrix form,

AX = B

R₂ – R₁

R₃ – 5R₁

R₃ + 2R₂

Again converting into equations we get

X + y + z = 1

- 3y + 2z = 1

- 14 y = 0

Y = 0

- 3 × 0 + 2z = 1

Z =

X + 0 + = 1

X =

∴