Cofactors, Adjoint, Inverse using Determinants

Grade 12 Maths Higher — Cofactors, Adjoint, Inverse using Determinants: 25 practice questions with instant scoring and explanations.

1. The minor Mᵢⱼ of element aᵢⱼ is the determinant obtained by:
2. The cofactor Cᵢⱼ is related to minor Mᵢⱼ by:
3. The adjoint (or adjugate) of matrix A is:
4. For any square matrix A, A·adj(A) =
5. If A is invertible, then A⁻¹ =
6. For a 2×2 matrix [a b; c d], the adjoint is:
7. If A is 3×3 with det(A) = 5, and C₁₂ = 3, then adj(A) has element at position (2,1) as:
8. The rank of adj(A) for non-singular n×n matrix A is:
9. If det(A) = 0, then adj(A) is:
10. For matrix A, det(adj(A)) =
11. The cofactor expansion by row i is: det(A) =
12. If all elements of row i are 0 except aᵢⱼ, then det(A) =
13. For a diagonal matrix D, the cofactor C₁₁ equals:
14. The formula A⁻¹ = adj(A)/det(A) requires:
15. If A = [2 3; 1 4], then adj(A) =
16. For matrix A, adj(Aᵀ) = [adj(A)]ᵀ because:
17. If A is orthogonal, then adj(A) =
18. Cramer's rule for Ax = b uses:
19. For a 3×3 matrix, finding all 9 cofactors requires computing:
20. If adj(A) = [2 0; 0 2] and det(A) = 4, then A =
21. For singular matrix A, the equation A·adj(A) = 0 holds:
22. The term cofactor expansion is also called:
23. If C is the cofactor matrix of A, then adj(A) = Cᵀ because:
24. For any square matrix A: (adj(A))ᵀ = adj(A) only if:
25. Review question for Cofactors, Adjoint, Inverse using Determinants