Q35 of 98 Page 310

Solve each of the following systems of equations using matrix method.

x - y = 3;


2x + 3y + 4z = 17;


y + 2z = 7.



To find: - x , y , z


Given set of lines are : -


x - y = 3


2x + 3y + 4z = 17


y + 2z = 7


Converting the following equations in matrix form,


AX = B



R2 – 2R1



2R3 - R2



Again converting into equations we get


X – y = 3


5y + 4z = 11


- 3y = 3


Y = - 1


5× - 1 + 4z = 11


4z = 16


Z = 4


X + 1 = 3


X = 2


∴ x = 2 , y = - 1 , z = 4


More from this chapter

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33

Solve each of the following systems of equations using matrix method.

5x - y = - 7;


2x + 3z = 1;


3y – z = 5.


 34

Solve each of the following systems of equations using matrix method.

x - 2y + z = 0;


y – z = 2;


2x – 3z = 10.


 36

Solve each of the following systems of equations using matrix method.

4x + 3y + 2z = 60;


x + 2y + 3z = 45;


6x + 2y + 3z = 70.


 37

If A = , find A - 1.

Using A - 1, solve the following system of equations:


2x – 3y + 5z = 11;


3x + 2y – 4z = - 5;


x + y – 2z = - 3.