Loading [MathJax]/jax/output/HTML-CSS/jax.js


1)

Let a, b and c be three real numbers satisfying [a b c][197827737]=[000]

 Let ω  be a solution of   x31=0  with  Im (ω) >0.If a=2  with b and c satisfying Eq (E). then the value of 3ωα+1ωb+3ωc


A) -2

B) 2

C) 3

D) -3

Answer:

Option A

Explanation:

 

 Given  ,[abc]1×3  [197827737]=[000]

  [a+8b+7c9a+2b+3c7a+7b+7c]=[000]

  a+8b+7c=0....(i)

  9a+2b+3c=0 .....(ii)

  a+b+c=0 .....(iii)

 On multiplying Eq.(iii) bt=y 2 , then substract from Eq.(ii) we get

 7a+c=0...(iv)

 Again multiplying Eq,(iii) by 3 , then substract from Eq.(ii) , we get

 6a-b=0....(v)

   b=6a and c=-7a

 if a=2,b=12 and c=-14

    3ωa+1ωb+3ωc

    3ω2+1ω12+3ω14

            =3ω2+1+3ω2

 =3ω+1+3ω2

=1+3(ω+ω2)

=1-3=-2