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

₹0.0

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

Options:

Correct Answer: -2

Exam Year: 2022

Solution:

Det(H) = (2*5) - (3*4) = 10 - 12 = -2.

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

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.

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