Find the value of `|(-8,6),(5,4)|`

Options

A. `-62`
B. `-30`
C. `-32`
D. `62`

Answer

To find the value of the determinant \(|(-8, 6), (5, 4)|\), we can follow these steps:

### Step 1: Write down the determinant
The determinant of a 2x2 matrix \(|(a, b), (c, d)|\) is calculated using the formula:
\[ |A| = ad - bc \]
In our case, we have:
\[ a = -8, \quad b = 6, \quad c = 5, \quad d = 4 \]

### Step 2: Substitute the values into the formula
Substituting the values into the determinant formula gives us:
\[ |(-8, 6), (5, 4)| = (-8)(4) - (6)(5) \]

### Step 3: Calculate the products
Now, we calculate the products:
\[ (-8)(4) = -32 \]
\[ (6)(5) = 30 \]

### Step 4: Subtract the second product from the first
Now, we perform the subtraction:
\[ -32 - 30 = -62 \]

### Step 5: Write the final answer
Thus, the value of the determinant \(|(-8, 6), (5, 4)|\) is:
\[ \boxed{-62} \]

---