What is the determinant of F = [[2, 0], [0, 3]]? (2023)

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Question: What is the determinant of F = [[2, 0], [0, 3]]? (2023)

Options:

Correct Answer: 6

Exam Year: 2023

Solution:

Determinant of F = (2*3) - (0*0) = 6.

What is the determinant of F = [[2, 0], [0, 3]]? (2023)

What is the determinant of F = [[2, 0], [0, 3]]? (2023)

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

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