Question

Solve the following systems of equations using matrix method. 

x – y + 2z = 7; 

3x + 4y – 5z = - 5: 

2x – y + 3z = 12.

Answer 1

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

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

∴ x = 2, y = 1. z = 3