Two sequences [a,\:b,\:c\:and\: [.A,\:B,\:C] are related as,{[ able A ; B ; C]}={[ able 1 , 1 , 1 ; 1 , w_3^{-1} , w_3^{-2} ; 1 , w_3^{-2} , w_3^{-4}]}{[ able a ; b ; c]} where w_3=e^{ {\j} \;{2 π}/{3}}If another sequence p,q,\:r is derived as, {[ able {\p} ; {\q} ; { }]}={[ able 1 , 1 , 1 ; 1 , {\w}_3^1 , {\w}_3^2 ; 1 , {\w}_3^2 , {\w}_3^4]}{[ able 1 , 0 , 0 ; 0 , {\w}_3^2 , 0 ; 0 , 0 , {\w}_3^4]}{[ able \;{ {\A}}/{3} ; \;{ {\B}}/{3} ; \;{ {\C}}/{3}]} Then the relationship between the sequences [p,\:q,\:r\:and\: [.a,\:b,\:c] \:is

Question

Two sequences  [a,\:b,\:c\:and\: [.A,\:B,\:C]   are related as,{[	able A ; B ; C]}={[	able 1 , 1 , 1 ; 1 , w_3^{-1} , w_3^{-2} ; 1 , w_3^{-2} , w_3^{-4}]}{[	able a ; b ; c]} where w_3=e^{ {\j} \;{2 π}/{3}}If another sequence p,q,\:r  is derived as,  {[	able  {\p} ;  {\q} ;  {}]}={[	able 1 , 1 , 1 ; 1 ,  {\w}_3^1 ,  {\w}_3^2 ; 1 ,  {\w}_3^2 ,  {\w}_3^4]}{[	able 1 , 0 , 0 ; 0 ,  {\w}_3^2 , 0 ; 0 , 0 ,  {\w}_3^4]}{[	able \;{ {\A}}/{3} ; \;{ {\B}}/{3} ; \;{ {\C}}/{3}]} Then the relationship between the sequences  [p,\:q,\:r\:and\: [.a,\:b,\:c] \:is

Examsnet · Accepted Answer

Correct Answer is : [p,q,r]=[c,a,b]

1	1	1
1	w3−1	w3−2
1	w3−2	w3−4

1	1	1
1	w31	w32
1	w32	w34

GATE Electronics and Communications (EC) 2015 Shift 1 Solved Paper