If F = [[2, 0], [0, 3]], what is det(F)? (2020)

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Question: If F = [[2, 0], [0, 3]], what is det(F)? (2020)

Options:

Correct Answer: 6

Exam Year: 2020

Solution:

The determinant of F is calculated as (2*3) - (0*0) = 6.

If F = [[2, 0], [0, 3]], what is det(F)? (2020)

If F = [[2, 0], [0, 3]], what is det(F)? (2020)

Step 1: Identify the matrix F, which is given as [[2, 0], [0, 3]].
Step 2: Recognize that F is a 2x2 matrix, where the elements are: a = 2, b = 0, c = 0, d = 3.
Step 3: Use the formula for the determinant of a 2x2 matrix, which is det(F) = (a * d) - (b * c).
Step 4: Substitute the values into the formula: det(F) = (2 * 3) - (0 * 0).
Step 5: Calculate the multiplication: 2 * 3 = 6 and 0 * 0 = 0.
Step 6: Subtract the second result from the first: 6 - 0 = 6.
Step 7: Conclude that the determinant of F is 6.

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