Evaluate \( \begin{vmatrix} x & 1 \\ 1 & y \end{vmatrix} \) when \( x =

Evaluate \( \begin{vmatrix} x & 1 \\ 1 & y \end{vmatrix} \) when \( x = 2 \) and \( y = 3 \).

Evaluate \( \begin{vmatrix} x & 1 \\ 1 & y \end{vmatrix} \) when \( x = 2 \) and \( y = 3 \).

Step 1: Identify the determinant formula for a 2x2 matrix, which is given by the formula: det(A) = ad - bc, where A = [[a, b], [c, d]].
Step 2: In our case, the matrix is [[x, 1], [1, y]]. Here, a = x, b = 1, c = 1, and d = y.
Step 3: Substitute the values of x and y into the formula. We have x = 2 and y = 3.
Step 4: Replace x and y in the determinant formula: det(A) = (2)(3) - (1)(1).
Step 5: Calculate (2)(3) which equals 6.
Step 6: Calculate (1)(1) which equals 1.
Step 7: Subtract the second result from the first: 6 - 1 = 5.
Step 8: The final result of the determinant is 5.

Determinants – The determinant of a 2x2 matrix is calculated using the formula ad - bc, where the matrix is represented as [[a, b], [c, d]].