Find the value of ' $k$ ', if $\left|\begin{array}{ccc} k-2 & 2 k-3 & 3 k-4 \ k-4 & 2 k-9 & 3 k-16 \ k-8 & 2 k-27 & 3 k-64 \end{array}\right|=0$

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Aicharya · Accepted Answer

It is given that, $\left|\begin{array}{ccc} k-2 & 2 k-3 & 3 k-4 \ k-4 & 2 k-9 & 3 k-16 \ k-8 & 2 k-27 & 3 k-64 \end{array}\right|=0$ On applying, $R_2 \longrightarrow R_2-R_1$ and $R_3 \longrightarrow R_3-R_1$, we get $\begin{aligned} & \Rightarrow \quad\left|\begin{array}{ccc} k-2 & 2 k-3 & 3 k-4 \ -2 & -6 & -12 \ -6 & -24 & -60 \end{array}\right|=0 \ & \Rightarrow \quad\left|\begin{array}{ccc} k-2 & 2 k-3 & 3 k-4 \ 1 & 3 & 6 \ 1 & 4 & 10 \end{array}\right|=0 \ & \Rightarrow \quad(k-2)[30-24]-(2 k-3)[10-6]+(3 k-4)[4-3]=0 \ & \Rightarrow \quad 6 k-12-8 k+12+3 k-4=0 \Rightarrow k=4 \end{aligned}$

Find the value of ' \(k\) ', if \(\left|\begin{array}{ccc} k-2 & 2 k-3 & 3 k-4 \\ k-4 & 2 k-9 & 3 k-16 \\…

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