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What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4

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Question: What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4, d = 5?

Options:

  1. -2
  2. 1
  3. 2
  4. 7

Correct Answer: 2

Solution: 

det = (2)(5) - (3)(4) = 10 - 12 = -2.

What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4

Practice Questions

Q1
What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4, d = 5?
  1. -2
  2. 1
  3. 2
  4. 7

Questions & Step-by-Step Solutions

What is the value of the determinant | a b | | c d | when a = 2, b = 3, c = 4, d = 5?
Correct Answer: -2
  • Step 1: Write down the values of a, b, c, and d. Here, a = 2, b = 3, c = 4, and d = 5.
  • Step 2: Set up the formula for the determinant of a 2x2 matrix: det = (a * d) - (b * c).
  • Step 3: Substitute the values into the formula: det = (2 * 5) - (3 * 4).
  • Step 4: Calculate (2 * 5) which equals 10.
  • Step 5: Calculate (3 * 4) which equals 12.
  • Step 6: Subtract the second result from the first: 10 - 12.
  • Step 7: The final result is -2.
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