If H = [[1, 2], [2, 4]], what is det(H)? (2020)

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Question: If H = [[1, 2], [2, 4]], what is det(H)? (2020)

Options:

Correct Answer: 0

Exam Year: 2020

Solution:

The determinant of H is (1*4) - (2*2) = 4 - 4 = 0.

If H = [[1, 2], [2, 4]], what is det(H)? (2020)

If H = [[1, 2], [2, 4]], what is det(H)? (2020)

Step 1: Identify the matrix H, which is given as H = [[1, 2], [2, 4]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is det([[a, b], [c, d]]) = (a * d) - (b * c).
Step 3: In our matrix H, a = 1, b = 2, c = 2, and d = 4.
Step 4: Substitute the values into the determinant formula: det(H) = (1 * 4) - (2 * 2).
Step 5: Calculate (1 * 4) which equals 4.
Step 6: Calculate (2 * 2) which equals 4.
Step 7: Subtract the second result from the first: 4 - 4 = 0.
Step 8: Conclude that the determinant of H is 0.

Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as (a*d) - (b*c).