Discuss the consistency of the following system of equations. Find the solution I consistant
x + y + z = 4
2x + y +z = 5
x-y+z=0
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Answer:
Given system of equations
x+y+z=1
2x+3y+2z=2
ax+ay+2az=4
This can be written as
AX=B
where A=
⎣
⎢
⎢
⎡
1
2
a
1
3
a
1
2
2a
⎦
⎥
⎥
⎤
,X=
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
,B=
⎣
⎢
⎢
⎡
1
2
4
⎦
⎥
⎥
⎤
Here, ∣A∣=1(6a−2a)−1(4a−2a)+1(2a−3a)
⇒∣A∣=a
=0
Since, ∣A∣
=0
Hence, the system of equations is consistent.
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