InterviewSolution
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Let three matrices A = [(-1,3,2),(2,-1,3),(1,2,3)], B = , C = [(-2,2,-1),(3,-5,4),(5,-6,4)] The value of log_(sqrt(8/7))[Tr^(2)(A) + +Tr^(3) ((ABC)/(2))+ Tr^(3) ((A(BC)^(2))/(2))+Tr^(3) ((A(BC)^(2))/(2))+.....+ oo] is [Note : Tr. (P) denote trace of matrix P] and Tr^(3)(A) = (Tr(A))^(3) |
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Answer» `-4` `TR(A) = -1 - 1 + 3 = 1` `Tr((ABC)/2) = Tr(A/2) = 1/2` `Tr^(2)(A) + +Tr^(3) ((ABC)/(2))+ Tr^(3) ((A(BC)^(2))/(2))+Tr^(3) ((A(BC)^(2))/(2))+.....+ oo` `= 1^(3) + (1/2)^(3) + (1/4)^(3) + (1/8)^(3) + oo` `= 1/(1 - 1/8) = 1/(7/8) = 8/7`. |
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