3.5-3.6 Determinants and inverse matrices Quiz: Pearson Edexcel Further Maths, Unit 3

The 20 questions

1. For a 3 x 3 matrix A and scalar k, what is det(kA)?

   • k det A
   • k^2 det A
   • k^3 det A
   • det A + k^3

2. When is a 3 x 3 matrix described as non-singular?

   • When it is symmetric
   • When its determinant is non-zero
   • When its trace is zero
   • When all its entries are non-zero

3. For an invertible matrix A, what is det(A^(-1))?

   • (det A)^2
   • -det A
   • 1 / det A
   • det A

4. For a 3 x 3 matrix with entries a_ij, which 2 x 2 determinant is the minor associated with entry a11?

   • a11 a22 - a12 a21
   • a21 a32 - a22 a31
   • a22 a33 + a23 a32
   • a22 a33 - a23 a32

5. If two rows of a 3 x 3 matrix are equal, what is its determinant?

   • -1
   • the sum of the rows
   • 1
   • 0

6. Which statement about determinants is always true for square matrices A and B of the same size?

   • det(A + B) = det A + det B
   • det(AB) = det A + det B
   • det(-A) = -det A for every 2 x 2 matrix A
   • det(AB) = det A x det B

7. What is the determinant of the matrix [[1, 2, 3], [0, 1, 4], [5, 6, 0]]?

   • 1
   • 2
   • 0
   • -1

8. What is the determinant of the diagonal matrix [[2, 0, 0], [0, 3, 0], [0, 0, 4]]?

   • 12
   • 9
   • 6
   • 24

9. What is the determinant of [[1, 0, 2], [0, 1, 0], [3, 0, 4]]?

   • -2
   • 4
   • -4
   • 2

10. A unit cube is transformed by the matrix diag(2, 1, 3). What is the volume of the image?

    • 1
    • 6
    • 5
    • 3

11. What is the determinant of [[1, 2, 3], [2, 4, 6], [0, 1, 1]]?

    • 1
    • 0
    • 2
    • -1

12. For the 2 x 2 matrix A = [[3, 1], [2, 4]], what is det(2A)?

    • 40
    • 80
    • 10
    • 20

13. A 3 x 3 matrix A has determinant 2. What is det(3A)?

    • 54
    • 6
    • 9
    • 18

14. A 2 x 2 matrix A has determinant 4. What is det(A^(-1))?

    • 4
    • 1/16
    • -1/4
    • 1/4

15. A system of three linear equations in three unknowns, written as Ax = b, has a unique solution when which condition holds?

    • b is the zero vector
    • A is symmetric
    • det A is zero
    • det A is not zero

16. What is the area of the triangle with vertices (0, 0), (1, 2) and (3, 1)?

    • 5
    • 2
    • 3/2
    • 5/2

17. For a 3 x 3 matrix A with det A = 5, what is det(2A^2)?

    • 100
    • 25
    • 200
    • 50

18. For what value of k is det [[1, 2, 0], [0, k, 1], [1, 0, 3]] equal to zero?

    • k = 3
    • k = 2/3
    • k = -2/3
    • k = -3/2

19. A 3 x 3 matrix A has det A = -4. Which statement describes the transformation it represents?

    • It collapses space onto a plane
    • It scales volumes by -4 and keeps orientation
    • It scales volumes by 1/4 and keeps orientation
    • It scales volumes by a factor of 4 and reverses orientation

20. What is the determinant of the matrix [[2, 1, 0], [1, 2, 1], [0, 1, 2]]?

    • 2
    • 4
    • 0
    • 6

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