If `A = |{:(1,1,-2),(2,1,-3),(5,4,-9):}|`, find |A|.

Explanation

To find the determinant of the matrix \( A = \begin{pmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{pmatrix} \), we will use the method of cofactor expansion along the first row (R1).

### Step 1: Write down the determinant expression
The determinant of matrix \( A \) can be expressed as:
\[ |A| = a_{11}C_{11} + a_{12}C_{12} + a_{13}C_{13} \]
where \( a_{ij} \) are the elements of the matrix and \( C_{ij} \) are the corresponding cofactors.
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