Lesson C1-C2

C1-C2 Matrix operations, zero and identity matrices Quiz: AQA Further Maths, Unit 2

20 questions

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Lesson C1-C2, Matrix operations, zero and identity matrices: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.

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The 20 questions

  1. What is the 2 x 2 identity matrix I?

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

  2. Which matrix is the 2 x 2 zero matrix?

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

  3. Which statement about the product AB, where A is 2 x 3 and B is 2 x 2, is correct?

    • AB is defined, since both matrices have 2 rows
    • AB is defined and has order 2 x 3
    • AB is defined and has order 2 x 2, since the result always has the size of B
    • AB is not defined, since the 3 columns of A do not match the 2 rows of B

  4. What is the order of the product of a 2 x 3 matrix and a 3 x 4 matrix?

    • 3 x 3
    • 2 x 4
    • 4 x 2
    • 2 x 3

  5. For A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], what is AB?

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

  6. For A = [[1, 0], [2, 1]] and B = [[1, 1], [0, 2]], what is 2A - 3B?

    • [[-1, -3], [4, -4]]
    • [[-1, -3], [4, 4]]
    • [[-1, 3], [4, -4]]
    • [[1, -3], [4, 4]]

  7. What is A^2 for A = [[2, 1], [0, 3]]?

    • [[5, 4], [0, 9]]
    • [[4, 3], [0, 9]]
    • [[4, 5], [0, 9]]
    • [[4, 2], [0, 6]]

  8. What is (3I)A for A = [[1, 2], [0, 4]]?

    • [[3, 6], [0, 12]]
    • [[3, 2], [0, 4]]
    • [[3, 6], [0, 4]]
    • [[4, 8], [0, 16]]

  9. A = [[1, 1], [1, 1]] and B = [[1, -1], [-1, 1]]. Which statement is correct?

    • AB is the identity matrix, since each row of A times each column of B gives one
    • AB = 2I, since the diagonal entries of A times B each give the value 2
    • AB is the zero matrix, although neither A nor B is the zero matrix
    • AB = BA, but both products are non-zero and equal to the identity matrix

  10. Which statement is always true for 2 x 2 matrices?

    • AB = BA for any A and B
    • AB = 0 implies A = 0 or B = 0
    • A^2 = 0 implies A = 0
    • AI = IA = A

  11. For what real x does [[x, 1], [1, x]] times [[1], [1]] equal [[3], [3]]?

    • x = 2
    • x = 4
    • x = 1
    • x = 3

  12. Find X satisfying 2X + I = [[3, 4], [5, 6]].

    • [[1, 2], [2, 2]]
    • [[1, 2], [2.5, 2.5]]
    • [[1.5, 2], [2.5, 3]]
    • [[2, 4], [5, 5]]

  13. For A = [[0, 1], [0, 0]], what is A^2?

    • A itself
    • The identity matrix
    • The zero matrix
    • [[0, 2], [0, 0]]

  14. For M = [[1, k], [0, 1]], what is M^3?

    • [[1, 3k], [0, 1]]
    • [[1, k^3], [0, 1]]
    • [[3, 3k], [0, 3]]
    • [[1, 2k], [0, 1]]

  15. Which matrix product is defined for A of order 3 x 2 and B of order 2 x 4?

    • BA, which has order 2 x 2
    • AB, which is not defined
    • AB, which has order 2 x 2
    • AB, which has order 3 x 4

  16. What is 4 times the matrix [[1, -1], [2, 0]]?

    • [[4, -4], [8, 0]]
    • [[4, -1], [2, 0]]
    • [[5, 3], [6, 4]]
    • [[4, -4], [2, 0]]

  17. What is the product AB for A = [[1, 2], [0, 1]] and B = [[1, 0], [3, 1]]?

    • [[1, 2], [3, 1]]
    • [[7, 2], [3, 1]]
    • [[7, 3], [2, 1]]
    • [[7, 2], [0, 1]]

  18. Which matrix is 2I - [[1, 0], [0, 3]]?

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

  19. Solve [[1, 2], [0, 1]] times [[x], [y]] equals [[5], [2]].

    • x = 3, y = 1
    • x = 2, y = 1
    • x = 1, y = 2
    • x = 5, y = 2

  20. What is the zero matrix multiplied by any 2 x 2 matrix?

    • The 2 x 2 zero matrix
    • The matrix itself
    • The 2 x 2 matrix with all entries 1
    • The identity matrix

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