What is the value of the determinant of the matrix [[1, 2], [3, 4]]?

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Question: What is the value of the determinant of the matrix [[1, 2], [3, 4]]?

Options:

Correct Answer: -2

Solution:

The determinant is calculated as (1*4) - (2*3) = 4 - 6 = -2.

What is the value of the determinant of the matrix [[1, 2], [3, 4]]?

What is the value of the determinant of the matrix [[1, 2], [3, 4]]?

Step 1: Identify the elements of the matrix. The matrix is [[1, 2], [3, 4]]. This means: a = 1, b = 2, c = 3, d = 4.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is det = (a * d) - (b * c).
Step 3: Substitute the values into the formula: det = (1 * 4) - (2 * 3).
Step 4: Calculate the first part: 1 * 4 = 4.
Step 5: Calculate the second part: 2 * 3 = 6.
Step 6: Subtract the second part from the first part: 4 - 6 = -2.
Step 7: The value of the determinant is -2.

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