Without expanding evaluate the determinant `|[41,1,5],[79,7,9],[29,5,3]|`

Explanation

To evaluate the determinant \( | \begin{bmatrix} 41 & 1 & 5 \\ 79 & 7 & 9 \\ 29 & 5 & 3 \end{bmatrix} | \) without expanding, we can use column operations to simplify the determinant.

### Step 1: Apply Column Operations
We will perform the operation \( C_1 \leftarrow C_1 - 8C_3 - C_2 \). This means we will subtract 8 times the third column and the second column from the first column.

### Calculation of New First Column:
- For the first row:
\[
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