If C = [[0, 1], [1, 0]], what is det(C)? (2022)

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Question: If C = [[0, 1], [1, 0]], what is det(C)? (2022)

Options:

Correct Answer: -1

Solution:

Determinant of C = (0*0) - (1*1) = 0 - 1 = -1.

If C = [[0, 1], [1, 0]], what is det(C)? (2022)

If C = [[0, 1], [1, 0]], what is det(C)? (2022)

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

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