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What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)

Practice Questions

Q1
What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)
  1. -2
  2. 2
  3. 1
  4. 7

Questions & Step-by-Step Solutions

What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)
  • Step 1: Identify the elements of the matrix J. The matrix J is [[2, 3], [4, 5]].
  • Step 2: Label the elements of the matrix. Let a = 2, b = 3, c = 4, d = 5.
  • Step 3: Use the formula for the determinant of a 2x2 matrix, which is det(J) = (a * d) - (b * c).
  • Step 4: Substitute the values into the formula: det(J) = (2 * 5) - (3 * 4).
  • Step 5: Calculate the first part: 2 * 5 = 10.
  • Step 6: Calculate the second part: 3 * 4 = 12.
  • Step 7: Subtract the second part from the first part: 10 - 12 = -2.
  • Step 8: Conclude that the determinant of the matrix J is -2.
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