10
Test the consistency of the system of linear equations
4x - 5y + z = 2
3x + y - 2z = 9
x + 4y + z = 5
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ANSWER
x−4y+7z=g..........(i)
0x+3y−5z=h..........(ii)
−2x+5y−9z=k...........(iii)
System of linear equation is consistent.
Δ=
∣
∣
∣
∣
∣
∣
∣
∣
1
0
−2
−4
3
5
7
−5
−9
∣
∣
∣
∣
∣
∣
∣
∣
=0
Then Δ
1
must be 0,
Therefore, Δ
1
=
∣
∣
∣
∣
∣
∣
∣
∣
g
h
k
−4
3
5
7
−5
−9
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒g[−27+25]+4[−9h+5k]+7[5h−3k]=0
⇒−2g−h−k=0
⇒2g+h+k=0
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