Question

Solve the following systems of equations using matrix method. 

3X + 4y + 7z = 4; 

2x – y + 3z = - 3; 

x + 2y – 3z = 8.

Answer 1

To find: - x , y , z 

Given set of lines are : - 

3X + 4y + 7z = 4; 

2x – y + 3z = - 3; 

x + 2y – 3z = 8 

Converting the following equations in matrix form, 

AX = B

3R₂ – 2R₁ 

3R₃ – R₁

Again converting into equations we get 

3x + 4y + 7z = 4 

- 11y - 5z = - 17 

- 186z = 186 

Z = - 1 

- 11y + 5 = - 17 

- 11y = - 22 

Y = 2 

3x + 4×2 + 7× - 1 = 4 

3x = 4 - 8 + 7

x = 1

∴ x = 1, y = 2, z = -1