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Quiz Chapter 2: Matrices

10 questions · Form 5 Mathematics Bab 2: Matrices

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. The total cost of 2 notebooks and 3 pens is RM13, while 4 notebooks and 1 pen cost RM11. Which matrix equation models this scenario?

  1. A. [[2, 3], [4, 1]] [[x], [y]] = [[13], [11]]
  2. B. [[2, 4], [3, 1]] [[x], [y]] = [[13], [11]]
  3. C. [[2, 3], [1, 4]] [[x], [y]] = [[13], [11]]
  4. D. [[3, 2], [1, 4]] [[x], [y]] = [[13], [11]]
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Answer: A

Let x = price of notebook, y = price of pen. 2x + 3y = 13 and 4x + y = 11. Matrix: [[2, 3], [4, 1]] [[x], [y]] = [[13], [11]].

2. Calculate [[x, 2]] [[3], [x]] = [20]. Find the positive value of x.

  1. B. 4
  2. A. 5
  3. C. 2
  4. D. 10
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Answer: B

x(3) + 2(x) = 20 => 3x + 2x = 20 => 5x = 20 => x = 4.

3. Matrix M has order 2 × 3 and matrix N has order 3 × 4. What is the order of the product matrix MN?

  1. A. 2 × 4
  2. C. 3 × 3
  3. B. 4 × 2
  4. D. Cannot be multiplied
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Answer: A

For (2 × 3) × (3 × 4), inner dimensions match (3=3). The resulting matrix order is outer dimensions 2 × 4.

4. Given A = [[1, 3], [2, 4]] and B = [[-1, 2], [0, 5]]. Calculate A - 2B.

  1. B. [[3, -1], [2, -6]]
  2. A. [[3, -1], [2, -14]]
  3. C. [[2, 1], [2, -1]]
  4. D. [[-1, 1], [2, -6]]
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Answer: B

2B = [[-2, 4], [0, 10]]. A - 2B = [[1 - (-2), 3 - 4], [2 - 0, 4 - 10]] = [[3, -1], [2, -6]].

5. If [x + 2 5] = [7 y - 1], find the values of x and y.

  1. C. x = 9, y = 4
  2. A. x = 5, y = 6
  3. B. x = 5, y = 4
  4. D. x = 7, y = 5
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Answer: A

Equating corresponding elements: x + 2 = 7 => x = 5; y - 1 = 5 => y = 6.

6. Convert the simultaneous equations 2x - 3y = 7 and x + 4y = -2 into matrix equation form AX = B.

  1. A. [[2, -3], [1, 4]] [[x], [y]] = [[7], [-2]]
  2. B. [[2, 3], [1, 4]] [[x], [y]] = [[7], [-2]]
  3. C. [[2, 1], [-3, 4]] [[x], [y]] = [[7], [-2]]
  4. D. [[2, -3], [4, 1]] [[x], [y]] = [[7], [-2]]
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Answer: A

The coefficient matrix contains coefficients of x and y: Row 1 = [2, -3], Row 2 = [1, 4].

7. What is the order of a matrix with 3 rows and 2 columns?

  1. B. 2 × 3
  2. A. 3 × 2
  3. C. 3 × 3
  4. D. 6
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Answer: A

The order of a matrix is written as rows × columns. 3 rows and 2 columns give order 3 × 2.

8. Find the product of [[1, 2], [3, 4]] and [[1], [0]].

  1. C. [[1, 2], [3, 0]]
  2. A. [[1], [3]]
  3. B. [[3], [7]]
  4. D. [[2], [4]]
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Answer: A

Row 1: 1(1) + 2(0) = 1. Row 2: 3(1) + 4(0) = 3. Result = [[1], [3]].

9. Given A B = I, where I is an identity matrix. Which statement is TRUE?

  1. A. B is the inverse matrix of A
  2. B. A and B are both column matrices
  3. C. det(A) = 0
  4. D. A + B = I
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Answer: A

By definition, if A B = I, then B = A⁻¹ (B is the inverse matrix of A).

10. Given matrix A = [4 -2 5]. What type of matrix is A?

  1. C. Square matrix
  2. A. Column matrix
  3. B. Row matrix
  4. D. Identity matrix
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Answer: B

Matrix A consists of a single row, so it is a row matrix (order 1 × 3).

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