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 gives the area scale factor of a linear transformation represented by a 2 x 2 matrix?

   • The sum of all four entries
   • The determinant, taken as its absolute value
   • The largest entry of the matrix
   • The trace, which is the sum of the diagonal entries

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

   • -1
   • 2
   • 1
   • 0

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

   • The transformation collapses the plane onto a line
   • The transformation is a translation
   • The transformation reverses orientation, as for a reflection
   • The transformation is an enlargement only

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. Let A = [[1, 0], [0, -1]] and B = [[0, -1], [1, 0]]. What single transformation is represented by AB?

    • Rotation of 90 degrees clockwise
    • Reflection in the line y = x
    • Reflection in the line y = -x
    • Rotation of 90 degrees anticlockwise

11. For the matrix [[2, 0], [0, 3]], which points are invariant?

    • The whole plane
    • The points (1, 1) and (2, 3)
    • Only the origin
    • Every point on the x-axis

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

    • The lines x = 1 and y = 1
    • The x-axis and the y-axis
    • Only the x-axis
    • The lines y = x and y = -x

13. For M = [[1, 1], [0, 2]], which points are fixed pointwise?

    • Every point (t, 0) on the x-axis
    • Only the line y = x
    • Every point on the y-axis
    • Only the origin

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 has determinant -3 and acts on a triangle of area 4. What are the new area and orientation?

    • Area 12 and orientation kept
    • Area 4/3 and orientation kept
    • Area 1/3 and orientation reversed
    • Area 12 and orientation reversed

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 are invariant under the transformation with matrix [[1, 2], [2, 1]]?

    • Every point on the line y = x
    • Every point on the line y = -x
    • Only the origin
    • All points on both lines y = x and y = -x

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

    • 5
    • -5
    • -6
    • 6

Related quizzes

• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Determinants and inverse matrices Quiz · 3.5-3.6 · 20 questions
• Solving three linear equations Quiz · 3.7-3.8 · 20 questions
• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions