Find the determinant of H = [[3, 1], [2, 5]]. (2021)

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Question: Find the determinant of H = [[3, 1], [2, 5]]. (2021)

Options:

Correct Answer: 7

Solution:

Determinant of H = (3*5) - (1*2) = 15 - 2 = 13.

Find the determinant of H = [[3, 1], [2, 5]]. (2021)

Find the determinant of H = [[3, 1], [2, 5]]. (2021)

Step 1: Identify the matrix H, which is [[3, 1], [2, 5]].
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 = 1, c = 2, d = 5.
Step 4: Substitute the values into the formula: det(H) = (3*5) - (1*2).
Step 5: Calculate the first part: 3*5 = 15.
Step 6: Calculate the second part: 1*2 = 2.
Step 7: Subtract the second part from the first part: 15 - 2 = 13.
Step 8: The determinant of H is 13.

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