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Matrices and determinants

Written by Hassan Raza (Mathematics)

Class 9 · Mathematics · 19 questions

Name: ____________________   Date: ____________

  1. A matrix with 3 rows and 2 columns has order:

    • A 3 x 3
    • B 3 x 2
    • C 6
    • D 2 x 3

  2. What is the determinant of the matrix [[2, 3], [1, 4]]?

    • A 8
    • B 11
    • C -5
    • D 5

  3. If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], what is A + B?

    • A [[1, 2], [3, 4]]
    • B [[1, 3], [4, 4]]
    • C [[1, 3], [4, 5]]
    • D [[0, 2], [3, 0]]

  4. A matrix whose determinant is zero is called:

    • A Identity
    • B Singular
    • C Non-singular
    • D Diagonal

  5. What is the transpose of [[1, 2, 3]]?

    • A [[3, 2, 1]]
    • B [[1], [2], [3]]
    • C [[1, 2, 3]]
    • D [[0]]

  6. What is 3 times the matrix [[1, 2], [0, 1]]?

    • A [[3, 2], [0, 1]]
    • B [[4, 5], [3, 4]]
    • C [[1, 6], [0, 3]]
    • D [[3, 6], [0, 3]]

  7. A matrix with only one row is called a:

    • A Row matrix
    • B Column matrix
    • C Square matrix
    • D Null matrix

  8. The identity matrix of order 2 is:

    • A [[0, 1], [1, 0]]
    • B [[1, 1], [1, 1]]
    • C [[0, 0], [0, 0]]
    • D [[1, 0], [0, 1]]

  9. If A = [[1, 2], [3, 4]], then 2A is:

    • A [[1, 4], [3, 8]]
    • B [[3, 4], [5, 6]]
    • C [[2, 4], [6, 8]]
    • D [[2, 2], [3, 4]]

  10. A matrix with the same number of rows and columns is:

    • A Square
    • B Row
    • C Zero
    • D Column

  11. Two matrices can be added only if they:

    • A Have the same determinant
    • B Have the same order
    • C Are square matrices
    • D Are identity matrices

  12. If A is 2 × 3 and B is 3 × 4, the order of AB is:

    • A 4 × 2
    • B 2 × 4
    • C 3 × 3
    • D 2 × 3

  13. The determinant of the matrix with rows (2, 3) and (1, 4) is:

    • A −5
    • B 8
    • C 11
    • D 5

  14. A matrix is singular when its determinant is:

    • A Zero
    • B Equal to its order
    • C One
    • D Negative

  15. The identity matrix of order 2 has diagonal entries:

    • A 0 and 0
    • B 1 and 0
    • C 1 and 1
    • D 2 and 2

  16. The transpose of a matrix is formed by:

    • A Swapping the signs of all entries
    • B Changing rows into columns
    • C Adding the rows
    • D Multiplying all entries by 2

  17. The adjoint of the matrix with rows (a, b) and (c, d) has rows:

    • A (d, −b) and (−c, a)
    • B (−a, −b) and (−c, −d)
    • C (d, b) and (c, a)
    • D (a, c) and (b, d)

  18. If |A| = 4 and adj A is known, then A⁻¹ equals:

    • A 4 ÷ adj A
    • B adj A − 4
    • C adj A ÷ 4
    • D 4 × adj A

  19. Which matrix has no inverse?

    • A The matrix with rows (2, 4) and (1, 2)
    • B The matrix with rows (3, 1) and (2, 1)
    • C The matrix with rows (1, 2) and (3, 5)
    • D The matrix with rows (1, 0) and (0, 1)

Answer key

1. B, 2. D, 3. B, 4. B, 5. B, 6. D, 7. A, 8. D, 9. C, 10. A, 11. B, 12. B, 13. D, 14. A, 15. C, 16. B, 17. A, 18. C, 19. A

  1. Order is written as rows x columns, so it is 3 x 2.

  2. det = 2 x 4 - 3 x 1 = 8 - 3 = 5.

  3. Add corresponding entries: [[1+0, 2+1], [3+1, 4+0]] = [[1, 3], [4, 4]].

  4. A matrix with determinant 0 is singular and has no inverse.

  5. The transpose swaps rows and columns, so a row matrix becomes a column matrix.

  6. Multiply each entry by 3.

  7. It has one row.

  8. Ones on the main diagonal and zeros elsewhere.

  9. Multiply each entry by 2.

  10. This is a square matrix.

  11. The entries must match in position.

  12. (2 × 3)(3 × 4) gives 2 × 4.

  13. (2)(4) − (3)(1) = 5.

  14. A zero determinant means the matrix is singular.

  15. The main diagonal is all ones.

  16. Rows become columns.

  17. Swap the diagonal entries and change the signs of the others.

  18. The inverse is the adjoint divided by the determinant.

  19. Its determinant is (2)(2) − (4)(1) = 0, so it is singular.