C5, C6, C9 Determinants, inverse matrices and factorising determinants Quiz: AQA Further Maths, Unit 2

The 20 questions

1. What is det [[a, b], [c, d]]?

   • ad + bc
   • ad - bc
   • ac - bd
   • ab - cd

2. What is the determinant of a singular matrix?

   • Minus one
   • One
   • Zero
   • Non-zero

3. For A = [[a, b], [c, d]] with ad - bc not zero, what is A^-1?

   • (1/(ad - bc)) [[a, b], [c, d]]
   • (1/(ad + bc)) [[d, b], [c, a]]
   • (1/(ad - bc)) [[d, -b], [-c, a]]
   • (1/(ad - bc)) [[-d, b], [c, -a]]

4. What is det [[2, 3], [1, 4]]?

   • -5
   • 3
   • 5
   • 11

5. What is det [[1, 2, 0], [0, 1, 3], [2, 0, 1]]?

   • 13
   • 11
   • -13
   • 7

6. What is the inverse of [[3, 1], [5, 2]]?

   • [[2, 1], [5, 3]]
   • [[3, -1], [-5, 2]]
   • [[2, -1], [-5, 3]]
   • [[-2, 1], [5, -3]]

7. What is the area scale factor of the matrix transformation [[2, 0], [1, 3]]?

   • 6
   • 3
   • 5
   • 2

8. What is the determinant of the matrix [[1, 2], [2, 4]]?

   • 8
   • 0
   • 1
   • 4

9. For what k is [[k, 2], [3, 4]] singular?

   • k = 2/3
   • k = 12
   • k = 3/2
   • k = 6

10. Which factorisation gives det [[1, a, a^2], [1, b, b^2], [1, c, c^2]]?

    • (b - a)(c - a)(c - b)
    • (b + a)(c + a)(c + b)
    • (b - a)(c - b)(c + a)
    • (a - b)(a - c)(b - c)

11. For which values of k is the matrix [[1, k], [k, 1]] singular?

    • k = 0
    • All real k
    • k = 1 or -1
    • k = 2 or -2

12. If det A = 4 for a 3 x 3 matrix A, what is det(2A)?

    • 64
    • 16
    • 8
    • 32

13. If det A = 3 and det B = -2, what is det(AB)?

    • -5
    • 1
    • -6
    • 6

14. What does det [[x, 1, 1], [1, x, 1], [1, 1, x]] factorise to?

    • (x - 1)(x + 2)^2
    • (x - 1)^2 (x - 2)
    • (x + 1)^2 (x - 2)
    • (x - 1)^2 (x + 2)

15. Why is the 3x3 matrix with rows [1,2,3], [2,4,6], and [1,0,1] singular?

    • Identity submatrix
    • Zero main diagonal
    • Negative determinant
    • Proportional rows

16. If A^-1 = [[1, 2], [0, 1]], what is A?

    • [[-1, -2], [0, -1]]
    • [[1, 0], [-2, 1]]
    • [[1, -2], [0, 1]]
    • [[1, 2], [0, 1]]

17. What is det [[4, 7], [2, 6]]?

    • -10
    • 22
    • 38
    • 10

18. What is the determinant of the 2 x 2 identity matrix?

    • -1
    • 0
    • 2
    • 1

19. A 3 x 3 matrix A has det A = 5. What is det(A^-1)?

    • 1/5
    • 1
    • -1/5
    • 5

20. What is the area scale factor for a matrix transformation with determinant -3?

    • 1/3
    • 9
    • -3
    • 3

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