3.3-3.4 Matrices as transformations and invariant points Quiz: Pearson Edexcel Further Maths, Unit 3

The 20 questions

1. Which 2 x 2 matrix represents reflection in the x-axis?

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

2. Which 2 x 2 matrix represents reflection in the line y = x?

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

3. Which 2 x 2 matrix represents a rotation of 90 degrees anticlockwise about the origin?

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

4. Which matrix represents an enlargement about the origin with scale factor k?

   • [[k, k], [k, k]]
   • [[1, k], [k, 1]]
   • [[k, 0], [0, 1]]
   • [[k, 0], [0, k]]

5. What quantity's absolute value gives the area scale factor of a 2 by 2 matrix transformation?

   • Eigenvalue
   • Determinant
   • Inverse
   • Trace

6. What is the determinant of a rotation matrix about the origin?

   • -1
   • 2
   • 1
   • 0

7. What does a negative matrix determinant indicate about a transformation?

   • Preserves orientation
   • Reduces area
   • Reverses orientation
   • Inverts direction

8. Under the transformation with matrix [[2, 1], [0, 3]], what is the image of the point (1, 2)?

   • (4, 6)
   • (4, 3)
   • (5, 6)
   • (2, 6)

9. What is the area scale factor of the transformation represented by [[2, 1], [0, 3]]?

   • 2
   • 3
   • 6
   • 5

10. What transformation does the matrix [[0, -1], [-1, 0]] represent?

    • Reflection in y-axis
    • Reflection in y = x
    • Reflection in y = -x
    • Reflection in x-axis

11. Which invariant points exist for the matrix [[2, 0], [0, 3]]?

    • All y-axis points
    • Every point
    • Origin only
    • All x-axis points

12. Which lines through the origin are invariant under matrix [[2, 0], [0, 3]]?

    • y-axis only
    • Both coordinate axes
    • x-axis only
    • Line y = x only

13. Which set of invariant points is fixed under matrix [[1, 1], [0, 2]]?

    • The x-axis
    • Line y = x
    • The y-axis
    • Origin only

14. For M = [[1, 1], [0, 2]], which line through the origin other than the x-axis is invariant?

    • x = 0
    • y = x
    • y = 2x
    • y = -x

15. The matrix [[3, 1], [2, 4]] transforms a unit square. What is the area of the image?

    • 10
    • 12
    • 5
    • 14

16. Under a shear represented by [[1, k], [0, 1]], what is the area scale factor?

    • 1 + k
    • 0
    • k
    • 1

17. A transformation with determinant -3 acts on a triangle of area 4. What is the new area?

    • 7
    • -12
    • 1.33
    • 12

18. Under the transformation M, the point (1, 0) maps to (-1, 0) and the point (1, 1) maps to (2, 2). Which is the image of (2, 0)?

    • (2, 0)
    • (4, 6)
    • (3, 2)
    • (-2, 0)

19. Which points remain invariant under matrix transformation [[1, 2], [2, 1]]?

    • Line y = x
    • Line y = -x
    • Origin only
    • All points

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

    • 5
    • -5
    • -6
    • 6

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