If J = [[1, 2], [2, 4]], what is det(J)? (2022)

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Question: If J = [[1, 2], [2, 4]], what is det(J)? (2022)

Options:

Correct Answer: 0

Exam Year: 2022

Solution:

Det(J) = (1*4) - (2*2) = 4 - 4 = 0.

If J = [[1, 2], [2, 4]], what is det(J)? (2022)

If J = [[1, 2], [2, 4]], what is det(J)? (2022)

Step 1: Identify the matrix J, which is J = [[1, 2], [2, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is det(J) = (a*d) - (b*c), where the matrix is [[a, b], [c, d]].
Step 3: Assign the values from the matrix J to a, b, c, and d: a = 1, b = 2, c = 2, d = 4.
Step 4: Substitute the values into the determinant formula: det(J) = (1*4) - (2*2).
Step 5: Calculate the first part: 1*4 = 4.
Step 6: Calculate the second part: 2*2 = 4.
Step 7: Subtract the second part from the first part: 4 - 4 = 0.
Step 8: Conclude that the determinant of matrix J is 0.

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