Evaluate `|{:(9,7,13),(4,3,9),(5,4,4):}|`

Answer

To evaluate the determinant \( | \begin{pmatrix} 9 & 7 & 13 \\ 4 & 3 & 9 \\ 5 & 4 & 4 \end{pmatrix} | \), we will follow a systematic approach.

### Step 1: Write down the determinant
We start with the given determinant:

\[ D = | \begin{pmatrix} 9 & 7 & 13 \\ 4 & 3 & 9 \\ 5 & 4 & 4 \end{pmatrix} | \]

### Step 2: Perform a row operation
We will perform a row operation to simplify the determinant. Let's subtract the third row from the first row:

\[ R_1 \rightarrow R_1 - R_3 \]

This gives us:

\[ D = | \begin{pmatrix} 9 - 5 & 7 - 4 & 13 - 4 \\ 4 & 3 & 9 \\ 5 & 4 & 4 \end{pmatrix} | \]

Calculating the first row:

\[ D = | \begin{pmatrix} 4 & 3 & 9 \\ 4 & 3 & 9 \\ 5 & 4 & 4 \end{pmatrix} | \]

### Step 3: Identify identical rows
Now we observe that the first row and the second row are identical:

\[ \begin{pmatrix} 4 & 3 & 9 \\ 4 & 3 & 9 \end{pmatrix} \]

### Step 4: Apply the property of determinants
According to the properties of determinants, if two rows (or columns) of a determinant are identical, the value of the determinant is zero. Therefore:

\[ D = 0 \]

### Final Answer
Thus, the value of the determinant is:

\[ \boxed{0} \]