Given the matrix A=[x-squareroot2009 , -1] [1 , x+squareroot2009] and I2, what is x if det(A)=0? [x-squareroot2009 , -1]-first row of matrix

To calculate the determinant of the matrix A, we'll have
to recall that the determinant of the square matrix (2x2) is the
following:

det(A) = a11*a22 -
a12*a21

a11*a22 - the elements that belong to the main
diagonal of the matrix

a12*a21 - the elemnents of the
secondary diagonal of the matrix

Therefore, det(A) =
(x-sqrt2009)(x+sqrt2009) - (-1)*1

We notice that the first
product returns the difference of two squares:

det(A) = x^2
- 2009 + 1

det(A) = x^2 -
2008

We'll cancel det
(A):

det(A) = 0 <=> x^2 - 2008 = 0 =>
x^2 = 2008

x1 = +sqrt2008

x2 =
-sqrt2008

The solutions of the equation
det(A)=0 are x1 = +sqrt2008 and x2 = -sqrt2008.