If A = [[1, 2], [3, 4]], what is the determinant of A?

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Question: If A = [[1, 2], [3, 4]], what is 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]], what is the determinant of A?

If A = [[1, 2], [3, 4]], what is the determinant of A?

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, which is (a*d) - (b*c).
Step 3: Assign the values from the matrix to the variables: a = 1, b = 2, c = 3, d = 4.
Step 4: Substitute the values into the formula: (1*4) - (2*3).
Step 5: Calculate 1*4, which equals 4.
Step 6: Calculate 2*3, which equals 6.
Step 7: Subtract the second result from the first: 4 - 6.
Step 8: The final result is -2, which is the determinant of matrix A.

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