Step 1:
To find the determinant of the 3x3 matrix, we use the formula:
\[
\left|\begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i
\end{array}\right| = a(ei - fh) - b(di - fg) + c(dh - eg)
\]
For the given matrix:
\[
\left|\begin{array}{ccc}
3 & -9 & 4 \\
1 & 4
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