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BARC OCES/DGFS Matrices & Determinants Questions with Answers & Explanations

20 Matrices & Determinants questions from the Engineering Mathematics section of BARC OCES/DGFS, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

What is the determinant of the matrix [[0, 4, 1], [-2, 3, 5], [0, 5, -1]]?

  1. A-18
  2. B-8
  3. C-16
  4. D-17
Show answer
Answer: (A) -18 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -18.
Question 2

What is the determinant of the matrix [[5, 0, 1], [-1, 1, 4], [3, 4, -2]]?

  1. A-91
  2. B-97
  3. C-95
  4. D-101
Show answer
Answer: (B) -97 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -97.
Question 3

What is the determinant of the matrix [[4, 4], [5, 0]]?

  1. A20
  2. B-20
  3. C16
  4. D-18
Show answer
Answer: (B) -20 det = ad − bc = (4)(0) − (4)(5) = -20.
Question 4

What are the eigenvalues of the matrix [[9, 6], [6, 9]]?

  1. A3 and 15
  2. B9 and 6
  3. C8 and 10
  4. D81 and 36
Show answer
Answer: (A) 3 and 15 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 5

What is the determinant of the matrix [[-2, 7], [-5, 7]]?

  1. A23
  2. B-49
  3. C-21
  4. D21
Show answer
Answer: (D) 21 det = ad − bc = (-2)(7) − (7)(-5) = 21.
Question 6

What is the determinant of the matrix [[2, -1], [-2, 6]]?

  1. A14
  2. B-10
  3. C10
  4. D12
Show answer
Answer: (C) 10 det = ad − bc = (2)(6) − (-1)(-2) = 10.
Question 7

What is the determinant of the matrix [[4, -2, 3], [1, -1, 0], [5, 3, -3]]?

  1. A31
  2. B32
  3. C30
  4. D28
Show answer
Answer: (C) 30 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 30.
Question 8

What are the eigenvalues of the matrix [[9, 3], [3, 9]]?

  1. A9 and 3
  2. B8 and 10
  3. C81 and 9
  4. D6 and 12
Show answer
Answer: (D) 6 and 12 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 9

What is the determinant of the matrix [[-1, 2, 5], [0, 4, 4], [-2, -2, 1]]?

  1. A14
  2. B12
  3. C6
  4. D13
Show answer
Answer: (B) 12 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 12.
Question 10

What is the determinant of the matrix [[5, 1], [4, 3]]?

  1. A11
  2. B-7
  3. C-11
  4. D13
Show answer
Answer: (A) 11 det = ad − bc = (5)(3) − (1)(4) = 11.

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Question 11

What are the eigenvalues of the matrix [[9, 6], [6, 9]]?

  1. A81 and 36
  2. B8 and 10
  3. C3 and 15
  4. D9 and 6
Show answer
Answer: (C) 3 and 15 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 12

What is the determinant of the matrix [[4, 3, 2], [4, 1, 0], [0, -3, 3]]?

  1. A-42
  2. B-50
  3. C-48
  4. D-58
Show answer
Answer: (C) -48 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -48.
Question 13

What is the determinant of the matrix [[-2, -1], [2, 6]]?

  1. A-8
  2. B-14
  3. C10
  4. D-10
Show answer
Answer: (D) -10 det = ad − bc = (-2)(6) − (-1)(2) = -10.
Question 14

What is the determinant of the matrix [[2, 5, 1], [-2, 2, -2], [-2, -1, 0]]?

  1. A32
  2. B18
  3. C22
  4. D20
Show answer
Answer: (C) 22 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 22.
Question 15

What is the determinant of the matrix [[1, -2], [4, -5]]?

  1. A5
  2. B3
  3. C-13
  4. D-3
Show answer
Answer: (B) 3 det = ad − bc = (1)(-5) − (-2)(4) = 3.
Question 16

What are the eigenvalues of the matrix [[5, 4], [4, 5]]?

  1. A4 and 6
  2. B25 and 16
  3. C5 and 4
  4. D1 and 9
Show answer
Answer: (D) 1 and 9 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 17

What is the determinant of the matrix [[1, 5, -2], [1, 3, 0], [0, -3, -2]]?

  1. A9
  2. B20
  3. C12
  4. D10
Show answer
Answer: (D) 10 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 10.
Question 18

What is the determinant of the matrix [[0, 4, -2], [-2, 4, 1], [4, 5, 2]]?

  1. A82
  2. B84
  3. C94
  4. D85
Show answer
Answer: (B) 84 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 84.
Question 19

What is the determinant of the matrix [[4, -4], [8, 6]]?

  1. A58
  2. B56
  3. C-64
  4. D-8
Show answer
Answer: (B) 56 det = ad − bc = (4)(6) − (-4)(8) = 56.
Question 20

What are the eigenvalues of the matrix [[3, 2], [2, 3]]?

  1. A9 and 4
  2. B2 and 4
  3. C3 and 2
  4. D1 and 5
Show answer
Answer: (D) 1 and 5 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.

These are RankerClub practice questions written in the BARC OCES/DGFS pattern. They are not official SSC/IBPS/RRB papers.

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