If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)

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Question: If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)

Options:

Correct Answer: 5

Exam Year: 2022

Solution:

The determinant of F is (2*3) - (1*1) = 6 - 1 = 5.

If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)

If F = [[2, 1], [1, 3]], what is the value of det(F)? (2022)

Step 1: Identify the matrix F. In this case, F = [[2, 1], [1, 3]].
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is det(F) = (a * d) - (b * c), where F = [[a, b], [c, d]].
Step 3: Assign the values from the matrix F to the variables a, b, c, and d. Here, a = 2, b = 1, c = 1, and d = 3.
Step 4: Substitute the values into the determinant formula: det(F) = (2 * 3) - (1 * 1).
Step 5: Calculate the first part: 2 * 3 = 6.
Step 6: Calculate the second part: 1 * 1 = 1.
Step 7: Subtract the second part from the first part: 6 - 1 = 5.
Step 8: Conclude that the value of det(F) is 5.

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