Find the determinant of F = [[4, 3], [2, 1]]. (2018)

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Question: Find the determinant of F = [[4, 3], [2, 1]]. (2018)

Options:

Correct Answer: -2

Exam Year: 2018

Solution:

Det(F) = (4*1) - (3*2) = 4 - 6 = -2.

Find the determinant of F = [[4, 3], [2, 1]]. (2018)

Find the determinant of F = [[4, 3], [2, 1]]. (2018)

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