If J = [[3, 1], [2, 4]], find det(J). (2023)

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Question: If J = [[3, 1], [2, 4]], find det(J). (2023)

Options:

Correct Answer: 10

Exam Year: 2023

Solution:

Det(J) = (3*4) - (1*2) = 12 - 2 = 10.

If J = [[3, 1], [2, 4]], find det(J). (2023)

If J = [[3, 1], [2, 4]], find det(J). (2023)

Step 1: Identify the elements of the matrix J. J = [[3, 1], [2, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix: det(J) = (a*d) - (b*c), where J = [[a, b], [c, d]].
Step 3: Assign the values from the matrix to the variables: a = 3, b = 1, c = 2, d = 4.
Step 4: Substitute the values into the determinant formula: det(J) = (3*4) - (1*2).
Step 5: Calculate the first part: 3*4 = 12.
Step 6: Calculate the second part: 1*2 = 2.
Step 7: Subtract the second part from the first part: 12 - 2 = 10.
Step 8: Conclude that the determinant of J is 10.

Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated using the formula det = (a*d) - (b*c).