The value of `|(441,442,443),(445,446,447),(449,450,451)|` is :

Options

A. `441 xx 446 xx 4510`
B. 0
C. `-1`
D. 1

Answer

To solve the determinant \( |(441, 442, 443), (445, 446, 447), (449, 450, 451)| \), we can follow these steps:

### Step 1: Write the Determinant
We start with the determinant:
\[ D = \begin{vmatrix} 441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451 \end{vmatrix} \]

### Step 2: Perform Column Operations
We can simplify the determinant by performing column operations.

**Operation 1:** Subtract the second column from the third column:
\[ C_3 \rightarrow C_3 - C_2 \]
This gives us:
\[ D = \begin{vmatrix} 441 & 442 & 1 \\ 445 & 446 & 1 \\ 449 & 450 & 1 \end{vmatrix} \]

**Operation 2:** Now, subtract the first column from the second column:
\[ C_2 \rightarrow C_2 - C_1 \]
This gives us:
\[ D = \begin{vmatrix} 441 & 1 & 1 \\ 445 & 1 & 1 \\ 449 & 1 & 1 \end{vmatrix} \]

### Step 3: Evaluate the Determinant
Now, we can see that the second and third columns are identical (both are \(1, 1, 1\)). According to the properties of determinants, if two columns are the same, the determinant is zero.

Thus, we have:
\[ D = 0 \]

### Final Answer
The value of the determinant \( |(441, 442, 443), (445, 446, 447), (449, 450, 451)| \) is:
\[ \boxed{0} \]

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