Solve each of the following systems of equations using matrix method.
2x + y - z = 1;
x – y + z = 2;
3x + y – 2z = - 1.
To find: - x , y , z
Given set of lines are : -
2x + y - z = 1
x - y + z = 2
3x + y - 2z = - 1
Converting the following equations in matrix form,
AX = B
2R2 – R1
2R3 – 3R1
3R3 - R2
Again converting into equations we get
2x + y – z = 1
- 3y + 3z = 3
- 6z = - 18
Z = 3
- 3y + 3×3 = 3
- 3y = 3 - 9
- 3y = - 6
Y = 2
2x + 2 - 3 = 1
2x = 1 + 1
X = 1
∴ x = 1 , y = 2 , z = 3