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GATE Matrices & Determinants Questions with Answers & Explanations

20 Matrices & Determinants questions from the Engineering Mathematics section of GATE, 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], [-2, 3]]?

  1. A6
  2. B8
  3. C-8
  4. D10
Show answer
Answer: (B) 8 det = ad − bc = (0)(3) − (4)(-2) = 8.
Question 2

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

  1. A-26
  2. B-28
  3. C-20
  4. D-25
Show answer
Answer: (A) -26 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -26.
Question 3

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

  1. A-6
  2. B-8
  3. C4
  4. D8
Show answer
Answer: (B) -8 det = ad − bc = (4)(-2) − (1)(0) = -8.
Question 4

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

  1. A5
  2. B21
  3. C10
  4. D11
Show answer
Answer: (D) 11 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 11.
Question 5

What are the eigenvalues of the matrix [[5, 2], [2, 5]]?

  1. A25 and 4
  2. B3 and 7
  3. C4 and 6
  4. D5 and 2
Show answer
Answer: (B) 3 and 7 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 6

What is the determinant of the matrix [[-1, -3], [7, 4]]?

  1. A-17
  2. B-25
  3. C19
  4. D17
Show answer
Answer: (D) 17 det = ad − bc = (-1)(4) − (-3)(7) = 17.
Question 7

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

  1. A88
  2. B90
  3. C92
  4. D94
Show answer
Answer: (B) 90 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 90.
Question 8

What are the eigenvalues of the matrix [[4, 3], [3, 4]]?

  1. A4 and 3
  2. B1 and 7
  3. C3 and 5
  4. D16 and 9
Show answer
Answer: (B) 1 and 7 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 9

What are the eigenvalues of the matrix [[8, 6], [6, 8]]?

  1. A8 and 6
  2. B2 and 14
  3. C7 and 9
  4. D64 and 36
Show answer
Answer: (B) 2 and 14 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 10

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

  1. A-72
  2. B-60
  3. C-62
  4. D-68
Show answer
Answer: (C) -62 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -62.

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Question 11

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

  1. A12
  2. B-10
  3. C-12
  4. D4
Show answer
Answer: (C) -12 det = ad − bc = (0)(-1) − (3)(4) = -12.
Question 12

What are the eigenvalues of the matrix [[6, 3], [3, 6]]?

  1. A36 and 9
  2. B5 and 7
  3. C3 and 9
  4. D6 and 3
Show answer
Answer: (C) 3 and 9 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 13

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

  1. A-30
  2. B-32
  3. C-34
  4. D-35
Show answer
Answer: (C) -34 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -34.
Question 14

What is the determinant of the matrix [[4, 4], [7, 1]]?

  1. A-22
  2. B9
  3. C24
  4. D-24
Show answer
Answer: (D) -24 det = ad − bc = (4)(1) − (4)(7) = -24.
Question 15

What are the eigenvalues of the matrix [[6, 5], [5, 6]]?

  1. A5 and 7
  2. B1 and 11
  3. C6 and 5
  4. D36 and 25
Show answer
Answer: (B) 1 and 11 For [[a, b], [b, a]] the eigenvalues are a − b and a + b.
Question 16

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

  1. A39
  2. B35
  3. C25
  4. D37
Show answer
Answer: (B) 35 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = 35.
Question 17

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

  1. A-6
  2. B-8
  3. C4
  4. D8
Show answer
Answer: (B) -8 det = ad − bc = (1)(-2) − (-2)(-3) = -8.
Question 18

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

  1. A-18
  2. B-20
  3. C-23
  4. D-22
Show answer
Answer: (D) -22 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -22.
Question 19

What is the determinant of the matrix [[7, -3], [7, -1]]?

  1. A16
  2. B-28
  3. C-14
  4. D14
Show answer
Answer: (D) 14 det = ad − bc = (7)(-1) − (-3)(7) = 14.
Question 20

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

  1. A-21
  2. B-20
  3. C-15
  4. D-19
Show answer
Answer: (D) -19 Expand along the first row: a(ek − fh) − b(dk − fg) + c(dh − eg) = -19.

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

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