For a square matrix
|a b |
|c d |
the determinant is given by (ad - bc)
In the problem the matrix given is:
|(2x+1) - 2 |
The determinant of the matrix is: (2x + 1)(2x - 1) - (-2)*(2x + 1)
=> (2x + 1)(2x - 1) + 2*(2x + 1)
4x^2 - 1 + 4x + 2
=> 4x^2 + 4x + 1
The required determinant is 4x^2 + 4x + 1
Since the given matrix is a square matrix, we may evaluate it's determinant.
Det A = a11*a22 - a12*a21
The determinant is the difference between the product of the terms located on the first diagonal (1st term from the 1st row* the 2nd term from the 2nd row) and the product of the terms located on the 2nd diagonal (2nd term from the 1st row *the 1st term from the 2nd row)
Let's identify the terms: a11 = (2x+1) ; a12 = (-2) ; a21 = (2x+1) and a22 = (2x-1).
Det A(x) = (2x+1)*(2x-1) - (-2)*(2x+1)
Det A = (2x+1)*(2x - 1 + 2)
Det A = (2x+1)*(2x + 1)
Det A = (2x+1)^2
The requested determinant of the square matrix A(x) is Det A = (2x+1)^2.