What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)

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Question: What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)

Options:

Correct Answer: -2

Exam Year: 2023

Solution:

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)

What is the determinant of the matrix J = [[2, 3], [4, 5]]? (2023)

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

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