Determinant Notation
`|(-3,-4),(-7,-6)|`

Answer

To find the value of the determinant given by the notation \( |(-3, -4), (-7, -6)| \), we will follow the steps outlined below:

### Step 1: Identify the elements of the determinant
The determinant is represented as:
\[ |a, b| = |(-3, -4), (-7, -6)| \]
Here, we can identify:
- \( a_1 = -3 \)
- \( b_1 = -4 \)
- \( a_2 = -7 \)
- \( b_2 = -6 \)

### Step 2: Apply the formula for a 2x2 determinant
The formula for the determinant of a 2x2 matrix is given by:
\[ \text{Determinant} = a_1 \cdot b_2 - a_2 \cdot b_1 \]
Substituting the identified values into the formula:
\[ \text{Determinant} = (-3) \cdot (-6) - (-7) \cdot (-4) \]

### Step 3: Calculate the products
Now, we calculate each term:
1. First term:
\[ (-3) \cdot (-6) = 18 \]
2. Second term:
\[ (-7) \cdot (-4) = 28 \]

### Step 4: Substitute back into the determinant formula
Now substitute these values back into the determinant formula:
\[ \text{Determinant} = 18 - 28 \]

### Step 5: Perform the final calculation
Now, calculate the final value:
\[ \text{Determinant} = 18 - 28 = -10 \]

### Conclusion
Thus, the value of the determinant \( |(-3, -4), (-7, -6)| \) is:
\[ \text{Determinant} = -10 \]

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