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


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