If H = [[0, 1], [-1, 0]], what is the determinant of H? (2019)

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Question: If H = [[0, 1], [-1, 0]], what is the determinant of H? (2019)

Options:

Correct Answer: -1

Exam Year: 2019

Solution:

The determinant of H is calculated as (0*-0) - (1*-1) = 0 + 1 = 1.

If H = [[0, 1], [-1, 0]], what is the determinant of H? (2019)

If H = [[0, 1], [-1, 0]], what is the determinant of H? (2019)

Step 1: Identify the matrix H, which is given as H = [[0, 1], [-1, 0]].
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 = 0, b = 1, c = -1, d = 0.
Step 4: Substitute the values into the determinant formula: det(H) = (0*0) - (1*-1).
Step 5: Calculate the first part: 0*0 = 0.
Step 6: Calculate the second part: 1*-1 = -1.
Step 7: Now, substitute these results back into the formula: det(H) = 0 - (-1).
Step 8: Simplify the expression: 0 + 1 = 1.
Step 9: Conclude that the determinant of H is 1.

Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated using the formula ad - bc.