The system of equations
2x+6y+11=0,6y-18z +1 = 0
6x + 20y - 6z + 3 = 0
1) is consistent 2) has unique solution
3) is inconsistent 4) cannot be determined
Answers
Answered by
0
Answer:
The given system of equations can be written as AX=B
where A=
⎣
⎢
⎢
⎡
2
0
6
6
6
20
0
−18
−6
⎦
⎥
⎥
⎤
, X=
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
,B=
⎣
⎢
⎢
⎡
−11
−1
−3
⎦
⎥
⎥
⎤
Here, D=∣A∣=
∣
∣
∣
∣
∣
∣
∣
∣
2
0
6
6
6
20
0
−18
−6
∣
∣
∣
∣
∣
∣
∣
∣
D=0
Now, D
1
=
∣
∣
∣
∣
∣
∣
∣
∣
−11
−1
−3
6
6
20
0
−18
−6
∣
∣
∣
∣
∣
∣
∣
∣
⇒D
1
=−3276
=0
As, D=0 and at least one of D
1
,D
2
,D
3
is non-zero, the system of equation is inconsistent and has no solution.
Hence, option 'C' is correct.
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