The determinant of a 2x2 matrix is given by the formula |Q| = ad - bc, where a, b, c, and d are the elements of the matrix Q arranged as follows:

Q = \( \left[ \begin{array}{cc} a & b \\ c & d \\ \end{array} \right]\)

In this case, the matrix Q is given as:

Q = \( \left[ \begin{array}{cc} 9 & -2 \\ -7 & 4 \\ \end{array} \right]\)

So, a = 9, b = -2, c = -7, and d = 4. Substituting these values into the formula for the determinant of a 2x2 matrix, we get:

|Q| = ad - bc

= (9)(4) - (-2)(-7)

= 36 - 14= 22

So, the determinant of the matrix Q is 22.