If J = [[1, 1], [1, 1]], what is det(J)? (2019)

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Question: If J = [[1, 1], [1, 1]], what is det(J)? (2019)

Options:

Correct Answer: 0

Exam Year: 2019

Solution:

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

If J = [[1, 1], [1, 1]], what is det(J)? (2019)

If J = [[1, 1], [1, 1]], what is det(J)? (2019)

Step 1: Identify the matrix J, which is given as J = [[1, 1], [1, 1]].
Step 2: Recall the formula for the determinant of a 2x2 matrix, which is det([[a, b], [c, d]]) = (a * d) - (b * c).
Step 3: In our matrix J, a = 1, b = 1, c = 1, and d = 1.
Step 4: Substitute the values into the determinant formula: det(J) = (1 * 1) - (1 * 1).
Step 5: Calculate the multiplication: (1 * 1) = 1 and (1 * 1) = 1.
Step 6: Now, subtract the second result from the first: 1 - 1 = 0.
Step 7: Therefore, the determinant of matrix J is det(J) = 0.

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).