Expand `|(3,2), (1,1)|`

Answer

To expand the determinant \( |(3, 2), (1, 1)| \), we can follow these steps:

1. **Set up the determinant**: We denote the determinant as \( \Delta \).
\[ \Delta = \begin{vmatrix} 3 & 2 \\ 1 & 1 \end{vmatrix} \]

2. **Apply the determinant formula for a 2x2 matrix**: The formula for the determinant of a 2x2 matrix \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \) is given by \( ad - bc \). Here, \( a = 3, b = 2, c = 1, d = 1 \).

3. **Substitute the values into the formula**:
\[ \Delta = (3 \times 1) - (2 \times 1) \]

4. **Calculate the products**:
\[ 3 \times 1 = 3 \]
\[ 2 \times 1 = 2 \]

5. **Subtract the second product from the first**:
\[ \Delta = 3 - 2 \]

6. **Final result**:
\[ \Delta = 1 \]

Thus, the value of the determinant \( |(3, 2), (1, 1)| \) is \( 1 \).