Lesson C5, C6, C9

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

20 questions

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Lesson C5, C6, C9, Determinants, inverse matrices and factorising determinants: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.

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The 20 questions

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

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

  2. A matrix is singular when its determinant is?

    • negative
    • one
    • zero
    • equal to its trace

  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. A transformation has matrix [[2, 0], [1, 3]]. Which describes its effect on area and orientation?

    • Area scale factor 6, orientation preserved
    • Area scale factor 1/6, orientation preserved
    • Area scale factor 6, orientation reversed
    • Area scale factor 5, orientation preserved

  8. Which is correct for [[1, 2], [2, 4]]?

    • Singular only when its entries are negative, and these entries are all positive
    • Singular, since its determinant is 0 and it has no inverse
    • Non-singular, since its entries are all positive so the determinant is not zero
    • Non-singular, with inverse [[1, 2], [2, 4]], since the matrix is its own inverse

  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 what values of k is [[1, k], [k, 1]] non-singular?

    • Only k = 1, since then the two rows of the matrix are the same
    • All real k, since the matrix is always non-singular
    • All real k except k = 1 and k = -1
    • Only k = 0, since the matrix is then the identity matrix

  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. Which statement about [[1, 2, 3], [2, 4, 6], [1, 0, 1]] is correct?

    • It has a unique inverse
    • It is non-singular, with determinant 2
    • It is singular only when the last row is zero
    • It is singular, since rows 1 and 2 are proportional

  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. A 2 x 2 matrix has determinant -3. What is true of its transformation?

    • Orientation is preserved and areas scale by a factor of -3
    • Orientation is reversed and areas are unchanged
    • Orientation is preserved and areas scale by a factor of 3
    • Orientation is reversed and areas scale by a factor of 3

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