What is the determinant of J = [[1, 2], [3, 5]]? (2020)

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Question: What is the determinant of J = [[1, 2], [3, 5]]? (2020)

Options:

Correct Answer: -1

Exam Year: 2020

Solution:

Det(J) = (1*5) - (2*3) = 5 - 6 = -1.

What is the determinant of J = [[1, 2], [3, 5]]? (2020)

What is the determinant of J = [[1, 2], [3, 5]]? (2020)

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

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