Calculate the determinant of H = [[3, 2], [1, 4]]. (2021)

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Question: Calculate the determinant of H = [[3, 2], [1, 4]]. (2021)

Options:

Correct Answer: 10

Exam Year: 2021

Solution:

Determinant of H = (3*4) - (2*1) = 12 - 2 = 10.

Calculate the determinant of H = [[3, 2], [1, 4]]. (2021)

Calculate the determinant of H = [[3, 2], [1, 4]]. (2021)

Step 1: Identify the matrix H, which is [[3, 2], [1, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix: det(H) = (a*d) - (b*c), where H = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 3, b = 2, c = 1, d = 4.
Step 4: Substitute the values into the formula: det(H) = (3*4) - (2*1).
Step 5: Calculate the first part: 3*4 = 12.
Step 6: Calculate the second part: 2*1 = 2.
Step 7: Subtract the second part from the first part: 12 - 2 = 10.
Step 8: Conclude that the determinant of H is 10.

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