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Question

If f(y)=∣ ∣ ∣(1y)a1b1(1y)a1b2(1y)a1b3(1y)a2b1(1y)a2b2(1y)a2b3(1y)a3b1(1y)a3b2(1y)a3b3∣ ∣ ∣ and a,b are even for i=1,2,3. then find f(2)

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Solution

If f(y)=∣ ∣ ∣a1b1(1y)a1b11a2b2(1y)a1b21a3b3(1y)a1b31(1y)a2b1(1y)a2b2(1y)a2b3(1y)a3b1(1y)a3b2(1y)a3b3∣ ∣ ∣+∣ ∣ ∣(1y)a1b1(1y)a1b2(1y)a1b3a2b1(1y)a2b11a2b2(1y)a2b21a2b3(1y)a2b31(1y)a3b1(1y)a3b2(1y)a3b3∣ ∣ ∣+∣ ∣ ∣(1y)a1b1(1y)a1b2(1y)a1b3(1y)a2b1(1y)a2b2(1y)a2b3a3b1(1y)a3b11a3b2(1y)a3b21a3b3(1y)a3b31∣ ∣ ∣

f(2)=∣ ∣a1b1a1b2a1b3111111∣ ∣+∣ ∣111a2b1a2b2a2b3111∣ ∣+∣ ∣111111a3b1a3b2a3b3∣ ∣

f(2)=0+0+0=0

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