DeterminantHard
Question
The determinant D = 
is divisible by
is divisible byOptions
A.1 + x
B.(1 + x)2
C.x2
D.x2 + 1
Solution
ᐃ = 
= a2b2c2
Applying C1 → C1 + C2 + C3
a2b2c2(3 + x)
Applying R1 → R1 - R2, R2 → R2 - R3
=
a2b2c2(3 + x)
= a2b2c2(3 + x) x2
Which is divisible by x2
= a2b2c2
Applying C1 → C1 + C2 + C3
a2b2c2(3 + x)
Applying R1 → R1 - R2, R2 → R2 - R3
=
a2b2c2(3 + x) = a2b2c2(3 + x) x2
Which is divisible by x2
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