Calculate the determinant of D = [[4, 2], [3, 1]]. (2020)

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Question: Calculate the determinant of D = [[4, 2], [3, 1]]. (2020)

Options:

Correct Answer: -2

Exam Year: 2020

Solution:

Determinant of D = (4*1) - (2*3) = 4 - 6 = -2.

Calculate the determinant of D = [[4, 2], [3, 1]]. (2020)

Calculate the determinant of D = [[4, 2], [3, 1]]. (2020)

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

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