Expand `|(2,4),(-5,-1)|`

Answer

To expand the determinant \(|(2, 4), (-5, -1)|\), we follow these steps:

1. **Identify the elements of the determinant**:
The determinant is given as:
\[ \begin{vmatrix} 2 & 4 \\ -5 & -1 \end{vmatrix} \]

2. **Apply the formula for a 2x2 determinant**:
The formula for the determinant of a 2x2 matrix \(\begin{vmatrix} a & b \\ c & d \end{vmatrix}\) is given by:
\[ ad - bc \]
Here, \(a = 2\), \(b = 4\), \(c = -5\), and \(d = -1\).

3. **Substitute the values into the formula**:
Now, substituting the values into the determinant formula:
\[ \text{Determinant} = (2 \cdot -1) - (4 \cdot -5) \]

4. **Calculate the products**:
Calculate each term:
\[ 2 \cdot -1 = -2 \]
\[ 4 \cdot -5 = -20 \]

5. **Combine the results**:
Now, substitute these results back into the determinant expression:
\[ \text{Determinant} = -2 - (-20) = -2 + 20 \]

6. **Final calculation**:
Finally, calculate the result:
\[ -2 + 20 = 18 \]

Thus, the value of the determinant \(|(2, 4), (-5, -1)|\) is \(18\).