Applications - Solving System of Linear Equations (Cramer's Rule)

Grade 12 Maths Higher — Applications - Solving System of Linear Equations (Cramer's Rule): 25 practice questions with instant scoring and explanations.

1. Cramer's rule can be applied to system AX = B when:
2. Using Cramer's rule, xᵢ =
3. In Cramer's rule, Aᵢ is the matrix obtained by replacing:
4. If det(A) = 0 and det(Aᵢ) ≠ 0 for some i, the system is:
5. For 2x + 3y = 5 and x - y = 1, using Cramer's rule: det(A) =
6. Cramer's rule gives the solution _____ directly without:
7. The computational complexity of Cramer's rule for n×n system is:
8. For homogeneous system AX = 0 with det(A) ≠ 0:
9. If |A| = 4 and |A₁| = 8, |A₂| = 4, then x =
10. Cramer's rule is suitable for:
11. The system 2x + 3y = 5, 4x + 6y = 10 has:
12. For system Ax = b, if rank(A) = rank([A|b]) < n, then:
13. Cramer's rule for 3×3 system requires computing:
14. If det(A) is very small but non-zero, Cramer's rule may be:
15. For system 3x - y = 7, 2x + y = 3, the value x =
16. The vector B in AX = B represents:
17. Cramer's rule fails when det(A) = 0 because:
18. For over-determined system (more equations than unknowns):
19. Under-determined system (more unknowns than equations):
20. The determinant |A₁| for system 2x + y = 5, 3x + 2y = 8 is:
21. For diagonal matrix A in AX = B, Cramer's rule simplifies to:
22. Parametric form of infinite solutions requires:
23. Cramer's rule works for complex coefficients:
24. For 3x + 2y + z = 11, x + y + z = 6, 2x - y + z = 3, the coefficient matrix determinant is:
25. Review question for Applications - Solving System of Linear Equations (Cramer's Rule)