$k$ ની કિમત . . . . માટે સમીકરણો $kx + 2y\,-z = 1$ ; $(k\,-\,1)y\,-2z = 2$ ; $(k + 2)z = 3$ એ એકાકી ઉકેલ ધરાવે .
Medium
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$D = \left| {\begin{array}{*{20}{c}}
k&2&{ - 1}\\
0&{k - 1}&{ - 2}\\
0&0&{k + 2}
\end{array}} \right| \ne 0\{ {\rm{for}}\,\,{\rm{unique}}\,\,{\rm{solution}}\Delta \ne {\rm{0\} }}$
k&2&{ - 1}\\
0&{k - 1}&{ - 2}\\
0&0&{k + 2}
\end{array}} \right| \ne 0\{ {\rm{for}}\,\,{\rm{unique}}\,\,{\rm{solution}}\Delta \ne {\rm{0\} }}$
$ \Rightarrow {\rm{k}}({\rm{k}} + 2)({\rm{k}} - 1) \ne 0 \Rightarrow {\rm{k}} \ne - 2,0,1$ so ${\rm{k}} = - 1$
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