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  4. If | beginmatrix 1 1 0 2 0 3 5 -6 x endmatrix |=29, then x is

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Q. If $ \left| \begin{matrix} 1 & 1 & 0 \\ 2 & 0 & 3 \\ 5 & -6 & x \\ \end{matrix} \right|=29, $ then $x$ is

J & K CETJ & K CET 2007Determinants

Solution:

Given, that, $ \left| \begin{matrix} 1 & 1 & 0 \\ 2 & 0 & 3 \\ 5 & -6 & x \\ \end{matrix} \right|=29 $
$ \Rightarrow $ $ 1(0+18)-1(2x-15)=29 $
$ \Rightarrow $ $ 18-2x+15=29 $
$ \Rightarrow $ $ 2x=4 $
$ \Rightarrow $ $ x=2 $