Q122
Two sequences [a, b, c] and [A, B, C] are related as, \[ [ array*20c A \\ B \\ C array ] = [ array*20c 1&1&1 \\ 1&W_3^ - 1&W_3^ - 2 \\ 1&W_3^ - 2&W_3^ - 4 array ] [ array*20c a \\ b \\ c array ]\] where, W_3 = e^i 2 3. If another sequence [p, q, r] is derived as, \[ [ array*20c a \\ b \\ c array ] = \] \[ [ array*20c 1&1&1 \\ 1&W_3^1&W_3^2 \\ 1&W_3^2&W_3^4 array ] [ array*20c 1&0&0 \\ 0&W_3^2&0 \\ 0&0&W_3^4 array ] [ array*20c A/3 \\ B/3 \\ C/3 array ]\] then the relationship between the sequences [p, q, r] and [a, b, c] is
Two sequences [a, b, c] and [A, B, C] are related as,
\left[ {\begin{array}{*{20}{c}} A \\ B \\ C \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^{ - 1}}&{W_3^{ - 2}} \\ 1&{W_3^{ - 2}}&{W_3^{ - 4}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] where,
If another sequence [p, q, r] is derived as,
\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{W_3^2}&0 \\ 0&0&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {A/3} \\ {B/3} \\ {C/3} \end{array}} \right]
then the relationship between the sequences [p, q, r] and [a, b, c] is
\left[ {\begin{array}{*{20}{c}} A \\ B \\ C \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^{ - 1}}&{W_3^{ - 2}} \\ 1&{W_3^{ - 2}}&{W_3^{ - 4}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] where,
If another sequence [p, q, r] is derived as,
\left[ {\begin{array}{*{20}{c}} a \\ b \\ c \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&{W_3^2}&0 \\ 0&0&{W_3^4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {A/3} \\ {B/3} \\ {C/3} \end{array}} \right]
then the relationship between the sequences [p, q, r] and [a, b, c] is
A.
[p, q, r] = [b, a, c]
B.
[p, q, r] = [b, c, a]
C.
[p, q, r] = [c, a, b]
AnswerD.
[p, q, r] = [c, b, a]
Answer: Option C
Solution
Answer: Option C
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