Solve the equation by method of reduction.
X + y + z= 1 2x + 3y +2z = 2 and x + y+ 2z = 4.
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Answer:
By writing in matrix
⎣
⎢
⎢
⎡
1
1
1
3
4
3
3
4
4
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
12
15
13
⎦
⎥
⎥
⎤
R
3
→R
3
−R
1
⎣
⎢
⎢
⎡
1
1
0
3
4
0
3
4
1
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
12
15
1
⎦
⎥
⎥
⎤
R
2
→R
2
−R
1
⎣
⎢
⎢
⎡
1
0
0
3
1
0
3
1
1
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
12
3
1
⎦
⎥
⎥
⎤
⇒x+3y+3z=12
y+z=3
z=1
⇒y+1=3
y=2
⇒x+3(2)+3(1)=12
x+6+3=12
x+9=12
x=3
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