Discuss the nature of system of equations and find there solution of equations
3w-6x-y-z=0
W-2x+5y-3z=0
2w-4x+3y-z=3
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Solution
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Correct option is
C
inconsistent
Given:
2x+6y+11=0
6x+20y−6z+3=0
6y−18z+1=0
Converting above equations in the determinant form, we get
Δ=
∣
∣
∣
∣
∣
∣
∣
∣
2
6
0
6
20
6
0
−6
−18
∣
∣
∣
∣
∣
∣
∣
∣
Here, Δ=−648+648=0
Now,
Δ
1
=
∣
∣
∣
∣
∣
∣
∣
∣
−11
−3
−1
6
20
6
0
−6
−18
∣
∣
∣
∣
∣
∣
∣
∣
Δ
1
=3276
=0
Δ
2
=
∣
∣
∣
∣
∣
∣
∣
∣
2
6
0
−11
−3
−1
0
6
−18
∣
∣
∣
∣
∣
∣
∣
∣
Δ
2
=−1092
=0
And Δ
3
=
∣
∣
∣
∣
∣
∣
∣
∣
2
6
0
6
20
6
−11
−3
−1
∣
∣
∣
∣
∣
∣
∣
∣
Δ
3
=−364
=0
So, here D=0 and no-one among D
1
,D
2
,D
3
is 0.
Hence, the system is inconsistent
Hence, option C.
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