4.03a-h Matrix language, linear transformations, invariance and determinants Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What geometrical factor does the absolute determinant of a 2D transformation matrix represent?

   • Length scale factor
   • Perimeter scale factor
   • Area scale factor
   • Volume scale factor

2. What is the determinant of any 2x2 singular matrix equal to?

   • -1
   • 0
   • Undefined
   • 1

3. Which transformation maps the point (x, y) to (-x, y) in two dimensions?

   • Rotation by 180°
   • Reflection in y = x
   • Reflection in y-axis
   • Reflection in x-axis

4. For a 3x3 matrix M, what is the determinant of 2M in terms of det M?

   • 8 det M
   • 4 det M
   • 6 det M
   • 2 det M

5. If matrix A represents transformation T1 and B represents T2, which matrix represents T1 followed by T2?

   • BA
   • A + B
   • AB
   • A - B

6. What is the relationship between det(A^-1) and det(A) for any non-singular matrix A?

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

7. What term describes a line where every individual point on the line is mapped to itself?

   • Line of symmetry
   • Eigenvector axis
   • Line of invariant points
   • Invariant line

8. What is the value of the determinant of any 2x2 identity matrix?

   • 1
   • -1
   • 2
   • 0

9. What is the determinant of the 2x2 matrix with top row [3, 2] and bottom row [1, 4]?

   • 10
   • 5
   • 11
   • 14

10. A shape with area 5 is transformed by a matrix with determinant 3. What is the new area?

    • 8
    • 15
    • 45
    • 2.5

11. Which matrix represents a reflection in the line y = x in 2D space?

    • [0, 1; 1, 0]
    • [0, -1; 1, 0]
    • [-1, 0; 0, 1]
    • [1, 0; 0, -1]

12. A 3D linear transformation has matrix determinant -4. What is its volume scale factor?

    • 64
    • -4
    • 4
    • 16

13. What is the determinant of the matrix product AB if det A = 3 and det B = -2?

    • 1
    • -6
    • -5
    • 6

14. Which point is always an invariant point under any 2D linear matrix transformation?

    • (1, 1)
    • (1, 0)
    • (0, 1)
    • (0, 0)

15. Which matrix represents an anticlockwise rotation of 90 degrees about the origin?

    • [0, 1; -1, 0]
    • [0, -1; 1, 0]
    • [-1, 0; 0, -1]
    • [0, 1; 1, 0]

16. What is the trace of the 2x2 matrix with top row [4, 1] and bottom row [2, 3]?

    • 5
    • 7
    • 10
    • 12

17. If the line y = 2x is an invariant line, where does (1, 2) map to?

    • (2k, k)
    • (k, -2k)
    • (k, 2k)
    • (1, -2)

18. What is the determinant of a square matrix whose columns are linearly dependent?

    • -1
    • 0
    • 3
    • 1

19. What matrix transformation is the inverse of a shear parallel to the x-axis with factor k?

    • Reflection in x-axis
    • Shear with factor -k
    • Stretch with factor -k
    • Shear with factor 1/k

20. If matrix A has determinant 5, what is the determinant of its transpose matrix A^T?

    • 25
    • -5
    • 5
    • 1/5

Related quizzes

• Proof by induction Quiz · 4.01 · 20 questions
• Complex numbers: language and arithmetic Quiz · 4.02a-d · 20 questions
• Modulus-argument form, polynomial roots and Argand diagrams Quiz · 4.02e-n · 20 questions
• Loci, de Moivre's theorem and roots of unity Quiz · 4.02o-s · 20 questions
• Matrix inverses, simultaneous equations and planes meeting Quiz · 4.03n-t · 20 questions
• Vector equations of lines and planes, scalar product Quiz · 4.04a-c · 20 questions
• Vector product, intersections and shortest distances Quiz · 4.04e-h · 20 questions
• Relationships between roots and coefficients; partial fractions Quiz · 4.05a-c · 20 questions
• Summation of series and the method of differences Quiz · 4.06a-b · 20 questions
• Hyperbolic functions, their derivatives and inverses Quiz · 4.07a-e · 20 questions