Let's say I have a matrix A:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A=\begin{bmatrix}

f(x)& z_1(x)& z_2(x)\\

0& a(x)& b(x)\\

0& c(x)& d(x)

\end{bmatrix}[/tex]

I've noticed that the determinant of A will either be [tex]a(x)d(x) - b(x)c(x)[/tex] or [tex]f(x)a(x)d(x)-f(x)b(x)c(x)[/tex]. I've never found an example of it taking another form. My question is, is there a way to determine which one it is? Does it depend soley on [tex]f(x)[/tex], or does it depend on all functions in the matrix?

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# Why would f(x) not be included in the determinant?

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