Expand `| (4,8),(6,7)|`

Answer

To expand the determinant \( | (4,8),(6,7)| \), we can follow these steps:

### Step 1: Write the determinant
We start with the determinant of the 2x2 matrix:
\[ \Delta = \begin{vmatrix} 4 & 8 \\ 6 & 7 \end{vmatrix} \]

### Step 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:
\[ \Delta = ad - bc \]
In our case, \( a = 4 \), \( b = 8 \), \( c = 6 \), and \( d = 7 \).

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ \Delta = (4 \times 7) - (8 \times 6) \]

### Step 4: Calculate the products
Calculating the products:
\[ \Delta = 28 - 48 \]

### Step 5: Simplify the expression
Now, simplify the expression:
\[ \Delta = -20 \]

### Final Answer
Thus, the value of the determinant \( | (4,8),(6,7)| \) is:
\[ \Delta = -20 \]

---