5.1 Multiplication of matrices Quiz: AQA Further Maths, Unit 5

The 20 questions

1. Multiply [[1, 2], [3, 4]] by [[0, 1], [1, 0]].

   • [[3, 4], [1, 2]]
   • [[0, 1], [1, 0]]
   • [[1, 2], [3, 4]]
   • [[2, 1], [4, 3]]

2. Multiply [[2, 0], [0, 3]] by [[1], [2]].

   • [[2], [3]]
   • [[2], [6]]
   • [[4], [6]]
   • [[3], [2]]

3. Multiply [[1, 2], [0, -1]] by the scalar 3.

   • [[3, 6], [0, -3]]
   • [[1, 5], [0, -1]]
   • [[3, 2], [0, -3]]
   • [[4, 5], [3, 2]]

4. A 2 x 2 matrix is multiplied by a 2 x 1 matrix. What size is the result?

   • 2 x 2
   • 2 x 1
   • Not defined
   • 1 x 2

5. Matrix A is 2 × 2 and matrix B is 2 × 1. What are the dimensions of AB?

   • 1 × 2
   • 2 × 1
   • Not defined
   • 2 × 2

6. Compute [[2, 1], [0, 1]] x [[1, 3], [2, 0]].

   • [[4, 6], [0, 0]]
   • [[4, 6], [2, 0]]
   • [[2, 6], [2, 1]]
   • [[3, 3], [2, 1]]

7. Compute [[1, 2], [3, 4]] x [[1], [1]].

   • [[4], [6]]
   • [[3], [7]]
   • [[2], [4]]
   • [[3], [4]]

8. Is matrix multiplication generally commutative (does AB always equal BA)?

   • No
   • Always
   • Yes
   • Only for 2 × 1

9. A transformation matrix is [[0, -1], [1, 0]]. What is its image of the column vector [3, 2]?

   • [[3], [-2]]
   • [[-3], [-2]]
   • [[2], [-3]]
   • [[-2], [3]]

10. Compute [[1, 4], [2, 3]] x [[2], [1]].

    • [[4], [7]]
    • [[5], [7]]
    • [[6], [5]]
    • [[6], [7]]

11. Find x and y if [[1, 2], [3, 4]] x [[x], [y]] = [[5], [11]].

    • x = 2, y = 1
    • x = 1, y = 3
    • x = 1, y = 2
    • x = 3, y = 1

12. For A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is the entry in row 1, column 2 of AB?

    • 19
    • 20
    • 22
    • 26

13. For A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is the entry in row 2, column 1 of AB?

    • 34
    • 41
    • 43
    • 38

14. For A = [[2, 1], [1, 1]], what is A^2?

    • [[5, 2], [3, 1]]
    • [[5, 3], [3, 2]]
    • [[4, 2], [2, 1]]
    • [[4, 1], [1, 1]]

15. Compute 2 x [[1, -1], [0, 3]].

    • [[2, -2], [0, 3]]
    • [[2, -2], [0, 6]]
    • [[1, -2], [0, 5]]
    • [[2, -1], [0, 6]]

16. A = [[a, 0], [0, 2]] and A x [[1], [1]] = [[3], [2]]. Find a.

    • 1
    • -3
    • 3
    • 2

17. Multiply [[1, 1], [0, 1]] by itself. What is the result?

    • [[1, 0], [0, 1]]
    • [[2, 2], [0, 2]]
    • [[1, 1], [0, 1]]
    • [[1, 2], [0, 1]]

18. Compute the entry in row 1, column 1 of [[2, 3], [1, 0]] x [[4, 1], [2, 5]].

    • 10
    • 14
    • 13
    • 11

19. Find the matrix X such that 2X = [[4, -2], [6, 0]].

    • [[4, -1], [6, 0]]
    • [[8, -4], [12, 0]]
    • [[2, -1], [3, 0]]
    • [[2, -2], [3, 0]]

20. Let A = [[1, 2], [0, 1]]. What is the entry in row 1, column 2 of A^3?

    • 3
    • 9
    • 8
    • 6

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