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If H = [[2, 3], [4, 5]], what is det(H)? (2022)

Practice Questions

Q1
If H = [[2, 3], [4, 5]], what is det(H)? (2022)
  1. -2
  2. 2
  3. 7
  4. 1

Questions & Step-by-Step Solutions

If H = [[2, 3], [4, 5]], what is det(H)? (2022)
  • Step 1: Identify the matrix H, which is H = [[2, 3], [4, 5]].
  • Step 2: Write down the formula for the determinant of a 2x2 matrix, which is det(H) = (a*d) - (b*c), where H = [[a, b], [c, d]].
  • Step 3: Assign the values from the matrix H to the variables: a = 2, b = 3, c = 4, d = 5.
  • Step 4: Substitute the values into the determinant formula: det(H) = (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 matrix H is det(H) = -2.
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