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

Answer

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

### Step 1: Set up the determinant
We define the determinant as:
\[ \Delta = |(1, 2), (4, 2)| \]
This can be represented in a 2x2 matrix form:
\[ \Delta = \begin{vmatrix} 1 & 2 \\ 4 & 2 \end{vmatrix} \]

### Step 2: Apply the determinant formula
For a 2x2 matrix \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \), the determinant is calculated using the formula:
\[ \text{Determinant} = ad - bc \]
In our case, \( a = 1 \), \( b = 2 \), \( c = 4 \), and \( d = 2 \).

### Step 3: Substitute the values into the formula
Now, substituting the values into the determinant formula:
\[ \Delta = (1)(2) - (2)(4) \]

### Step 4: Perform the multiplication
Calculating the products:
\[ \Delta = 2 - 8 \]

### Step 5: Simplify the expression
Now, we simplify the expression:
\[ \Delta = -6 \]

### Final Result
Thus, the expanded value of the determinant \( |(1, 2), (4, 2)| \) is:
\[ \Delta = -6 \]

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