LA2.1.16

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Solve for x given \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix}=0\,

By R_1-R_2,R_2-R_3\,

\begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix}=\begin{vmatrix} 2 & 6 & 12 \\ 4 & 18 & 48 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix}\,

By applying C_2-2C_1,C_3-3C_1\,

\begin{vmatrix} 2 & 2 & 6 \\ 4 & 10 & 36 \\ x-8 & -11 & -40 \end{vmatrix}\,

2(2)\begin{vmatrix} 1 & 1 & 3 \\ 2 & 5 & 18 \\ x-8 & -11 & -40 \end{vmatrix}\,

By R_2-2R_1,R_3+4R_2\,

4\begin{vmatrix} 1 & 1 & 3 \\ 0 & 3 & 12 \\ x & 9 & 32 \end{vmatrix}\,

Therefore 4[1(96-108)+x(12-9)]=0,3x-12=0,x=4\,


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