Step 1: Identify the elements of the matrix A. The matrix A is given as: | 1 2 | | 3 4 |.
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is: det(A) = (a)(d) - (b)(c), where a, b, c, and d are the elements of the matrix.
Step 3: Assign the values from the matrix to the variables in the formula. Here, 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 (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, so det(A) = -2.
Determinant of a 2x2 Matrix – The determinant of a 2x2 matrix A = | a b | | c d | is calculated using the formula det(A) = ad - bc.
