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Question

Given a matrix A=abcbcacab, where a, b, c are real positive numbers, abc = 1 and ATA = I, then find the value of a3+b3+c3.

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Solution

Given A=abcbcacab
Here, A=AT
Also, |A|=a(bca2)b(b2ac)+c(abc2)
|A|=3abca3b3c3
|A|=3a3b3c3 (abc=1 given)
Also, given AAT=I
A2=I
|A2|=1
|A|=±1
3a3b3c3=1 ( a, b,c are positive real numbers and 3abca3b3c3=(a+b+c)(a2+b2+c2abbcac))
a3+b3+c3=4

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