Find the determinant of F = [[4, 5], [6, 7]]. (2020)

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Question: Find the determinant of F = [[4, 5], [6, 7]]. (2020)

Options:

Correct Answer: -2

Solution:

Det(F) = (4*7) - (5*6) = 28 - 30 = -2.

Find the determinant of F = [[4, 5], [6, 7]]. (2020)

Find the determinant of F = [[4, 5], [6, 7]]. (2020)

Step 1: Identify the matrix F, which is [[4, 5], [6, 7]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is Det(F) = (a*d) - (b*c), where F = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 4, b = 5, c = 6, d = 7.
Step 4: Substitute the values into the determinant formula: Det(F) = (4*7) - (5*6).
Step 5: Calculate 4*7, which equals 28.
Step 6: Calculate 5*6, which equals 30.
Step 7: Subtract the second result from the first: 28 - 30.
Step 8: The result is -2, so the determinant of F is -2.

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