​ Let A = [aij] be a 3 × 3 matrix, where aij =1, if i = j -x, if |i - j| = 1 2x+1, otherwise. Let a function f : R → R be defined as f(x) = det(A).

Question

Let A = [a_ij] be a 3 × 3 matrix, where

a_ij = \(\begin{cases} 1, & if\, i=j \\ -x, & if\,|i-j|=1 \\ 2x+1, & otherwise. \end{cases}\)

1, if i = j

-x, if |i - j| = 1

2x+1, otherwise.

Let a function f : R → R be defined as f(x) = det(A). Then the sum of maximum and minimum values of f on R is equal to:

(1) -20/27

(2) 88/27

(3) 20/27

(4) -88/27

Answer 1

Answer is: (4) - 88/27