What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)

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Question: What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)

Options:

Correct Answer: -2

Exam Year: 2019

Solution:

The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.

What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)

What is the determinant of the matrix J = [[5, 6], [7, 8]]? (2019)

Step 1: Identify the elements of the matrix J. The matrix J is [[5, 6], [7, 8]].
Step 2: Label the elements of the matrix. Let a = 5, b = 6, c = 7, d = 8.
Step 3: Use the formula for the determinant of a 2x2 matrix, which is: determinant = (a * d) - (b * c).
Step 4: Substitute the values into the formula: determinant = (5 * 8) - (6 * 7).
Step 5: Calculate the first part: 5 * 8 = 40.
Step 6: Calculate the second part: 6 * 7 = 42.
Step 7: Subtract the second part from the first part: 40 - 42 = -2.
Step 8: Conclude that the determinant of the matrix J is -2.

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