Given a matrix `A=[a b c b c a c a b],w h e r ea ,b ,c` are real positive numbers `a b c=1a n dA^T A=I ,` then find the value of `a^3+b^3+c^3dot`

Answer

4

Explanation

`A^(1)A=I`
As `A^(T)=A`
`impliesA^(2)=I`
`impliesa^(2)+b^(2)=c^(2)=I` and `ab+bc+ca=0`
As `(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2(ab+bc+ca)`
`implies(a+b+c)=+-1`
Now `a^(3)+b^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
`impliesa^(3)+b^(3)-3=(a+b+c)`
`impliesa^(2)+b^(3)+c^(3)=3+-1`
`impliesa^(3)+b^(3)+c^(3)=4,2`