Applications of Matrices (solving equations)

Grade 12 Maths — Applications of Matrices (solving equations): 25 practice questions with instant scoring and explanations.

1. A system of linear equations Ax = b can be solved using matrices if:
2. If Ax = b and A is invertible, then x equals:
3. The system of equations 2x + 3y = 5 and 4x + 6y = 10 is:
4. For the matrix equation Ax = b, the matrix A is called:
5. A system Ax = b has a unique solution if and only if:
6. The augmented matrix for the system x + 2y = 3, 3x + 4y = 7 is:
7. Cramer's rule applies when:
8. For a 2 × 2 system with coefficient matrix A = [[2, 1], [1, 3]], the determinant is:
9. Row reduction of the augmented matrix helps to:
10. Gaussian elimination transforms the augmented matrix to:
11. The rank of the coefficient matrix compared to the augmented matrix determines:
12. Using the matrix method, to solve Ax = b, we multiply both sides by:
13. A homogeneous system Ax = 0 always has:
14. For a non-homogeneous system Ax = b, a particular solution is:
15. If Ax = b has a solution, then b is in the:
16. The null space of A consists of all vectors x such that:
17. For the system x + y + z = 6, 2x − y + z = 3, x + y − z = 0, in matrix form Ax = b:
18. Elementary row operations include:
19. The system is inconsistent if:
20. If rank(A) = rank([A|b]) = n, then the system has:
21. The system 3x + 2y = 5, 6x + 4y = 8 is:
22. By Cramer's rule, if det(A) = 2, det(Ax) = 4, det(Ay) = 6, then x and y are:
23. A matrix equation XA = B has solution X = BA⁻¹ if:
24. Question?
25. Question?