Question

Solve the following equations using matrix:-
x + 2y + z = 0
3x + y +z = 7
2x -y +z = 4​

Answer 1

Hello,

Given that,

x + 2y + z = 0 ___(1)

3x + y +z = 7_____(2)

2x -y +z = 4______(3)

Adding (2)&(3)

3x + y +z = 7_____(2)

+ 2x -y +z = 4______(3)

_______________________

5x+z=11______(4)

Adding (1) & (3) *2

x +2y + z = 0 ___(1)

+ 4x -2y +2z = 8______(3)

__________________________

5x+3z=8_______(5)

Solving (5) and (4)

We get,

Subtracting (5) from (4)

5x+3z=8_______(5)

- 5x-z=-11______(4)

______________________

2z=-3

z=-3/2

Substituting z in (4)

5x-(3/2)=11

10x-3=22

10x=25

x=5/2

Substituting x and z in (1)

(5/2) + 2y + (-3/2)= 0

y=-1/2

Therefore,

x=5/2, y=-1/2, z=-3/2

Hope this helps!