Calculate the determinant of the matrix [[1, 2], [3, 4]].

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Question: Calculate the determinant of the matrix [[1, 2], [3, 4]].

Options:

Correct Answer: -2

Solution:

Determinant = (1*4) - (2*3) = 4 - 6 = -2.

Calculate the determinant of the matrix [[1, 2], [3, 4]].

Calculate 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 determinant of the matrix is -2.

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