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If F = [[2, 0], [0, 3]], what is det(F)? (2020)

Practice Questions

Q1
If F = [[2, 0], [0, 3]], what is det(F)? (2020)
  1. 0
  2. 6
  3. 5
  4. 2

Questions & Step-by-Step Solutions

If F = [[2, 0], [0, 3]], what is det(F)? (2020)
  • Step 1: Identify the matrix F, which is given as [[2, 0], [0, 3]].
  • Step 2: Recognize that F is a 2x2 matrix, where the elements are: a = 2, b = 0, c = 0, d = 3.
  • Step 3: Use the formula for the determinant of a 2x2 matrix, which is det(F) = (a * d) - (b * c).
  • Step 4: Substitute the values into the formula: det(F) = (2 * 3) - (0 * 0).
  • Step 5: Calculate the multiplication: 2 * 3 = 6 and 0 * 0 = 0.
  • Step 6: Subtract the second result from the first: 6 - 0 = 6.
  • Step 7: Conclude that the determinant of F is 6.
  • Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated using the formula ad - bc.
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