Let `A=[3x^2 1 6x],B=[abc],a n dC=[(x+2)^2 5x^2 2x5x^2 2x(x+2)^2 2x(x+2)^2 5x^2]` be three given matrices, where `a ,b ,ca n dx in Rdot` Given that `f(x)=a x^2 +b x+c ,` then the value of `f(I)` is ______.

Answer

7

Explanation

We have `AB=[(3ax^(2),3bx^(2),3cx^(2)),(a,b,c),(6ax,6bx,6cx)]`
Now tr. `(AB)=` tr. (C)
`implies 3ax^(2)+b+6cx=(x+2)^(2)+2x+5x^(2) AA x in R` (Identity)
`implies 3ax^(2)+6cx+b=6x^(2)+6x+4`
`implies a=2, c=1, b=4`