Determinants - 2×2 and 3×3

Grade 12 Maths — Determinants - 2×2 and 3×3: 25 practice questions with instant scoring and explanations.

1. The determinant of a 2 × 2 matrix [[a, b], [c, d]] is:
2. For matrix A = [[2, 3], [1, 4]], det(A) equals:
3. A matrix is singular if:
4. For a 3 × 3 matrix, the determinant can be calculated using:
5. The determinant of the identity matrix I (any order) is:
6. The determinant of a zero matrix is:
7. If det(A) = 5, then det(kA) for a 3 × 3 matrix equals:
8. The determinant of a matrix A equals the determinant of A^T:
9. For the matrix [[1, 2, 3], [0, 4, 5], [0, 0, 6]], the determinant is:
10. The minor Mᵢⱼ is the determinant of the matrix obtained by:
11. The cofactor Cᵢⱼ equals:
12. Expanding a determinant along a row uses the formula:
13. If two rows of a matrix are identical, then det(A) equals:
14. If two columns of a matrix are swapped, the determinant:
15. For matrices A and B of the same order, det(AB) equals:
16. If matrix A is obtained from B by multiplying a row by k, then det(A) equals:
17. The determinant of an upper triangular matrix is:
18. For a matrix A, if det(A) ≠ 0, then A is:
19. If A is a 3 × 3 matrix and det(A) = 4, then det(2A) equals:
20. For the matrix [[2, 1], [−3, 4]], det(A) equals:
21. If a row of matrix A is a linear combination of other rows, then det(A) equals:
22. The determinant of an n × n matrix A equals 5. Then det(A^T) equals:
23. If det(A) = 0, then the system of equations Ax = b:
24. For an orthogonal matrix A, det(A) equals:
25. Solve 2x - y = 4, x + y = 5