To find: - x , y , z

Given set of lines are : -

x - y + 2z = 7

3x + 4y – 5z = - 5

2x – y + 3z = 12

Converting the following equations in matrix form,

AX = B

R₂ – 3R₁

R₃ – 2R₁

7R₃ - R₂

Again converting into equations we get

x – y + 2z = 7

7y - 11 z = - 26

4z = 12

Z = 3

7y – 11 ×3 = - 26

7y = - 26 + 33

7y = 7

Y = 1

X – 1 + 2×3 = 7

X = 7 + 1 - 6

X = 2

∴