1.

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)

Answer»

`-4`
`2`
`6`
`4`

Solution :`BC = [(4,-2,3),(8,-3,5),(7,-2,4)][(-2,2,-1),(3,-5,4),(5,-6,4)] = I`
`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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