Compute the determinant of the 2x2 matrix [ [3, 5], [2, 4] ].

Compute the determinant of the 2x2 matrix [ [3, 5], [2, 4] ].

• A. -2
• B. 6
• C. 0
• D. 2

Answer: (D)

The determinant of a 2x2 matrix with entries a, b in the first row and c, d in the second row is ad − bc. Here a = 3, b = 5, c = 2, d = 4. Compute ad = 3×4 = 12 and bc = 5×2 = 10, so the determinant is 12 − 10 = 2. Since the determinant is nonzero, the matrix is invertible, and the area of the parallelogram spanned by its column vectors is 2. The value 2 matches the given correct choice.

The determinant of a 2x2 matrix with entries a, b in the first row and c, d in the second row is ad − bc. Here a = 3, b = 5, c = 2, d = 4. Compute ad = 3×4 = 12 and bc = 5×2 = 10, so the determinant is 12 − 10 = 2. Since the determinant is nonzero, the matrix is invertible, and the area of the parallelogram spanned by its column vectors is 2. The value 2 matches the given correct choice.