1. **Problem:** Find the determinant of the matrix \(\begin{bmatrix} l & o \\ v & e \end{bmatrix}\). 2. **Formula:** The determinant of a 2x2 matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by: $$\det = ad - bc$$ 3. **Apply the formula:** Here, \(a = l\), \(b = o\), \(c = v\), and \(d = e\). So, $$\det = l \times e - o \times v$$ 4. **Explanation:** The determinant measures the scaling factor of the linear transformation represented by the matrix and can be calculated by multiplying the elements of the main diagonal and subtracting the product of the other diagonal. 5. **Final answer:** $$\boxed{\det = le - ov}$$