If A = [[1, 2], [3, 4]], find the determinant of A.

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Question: If A = [[1, 2], [3, 4]], find the determinant of A.

Options:

Correct Answer: 2

Solution:

The determinant of A is (1*4) - (2*3) = 4 - 6 = -2.

If A = [[1, 2], [3, 4]], find the determinant of A.

If A = [[1, 2], [3, 4]], find the determinant of A.

Correct Answer: -2

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

Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix A = [[a, b], [c, d]] is calculated using the formula ad - bc.