A) \[1\]
B) \[2\]
C) \[3\]
D) \[4\]
Correct Answer: C
Solution :
[c] \[\Delta =\left| \begin{matrix} X & SX & tX \\ {{X}_{1}} & S{{X}_{1}}+{{S}_{1}}X & t{{X}_{1}}+{{t}_{1}}X \\ {{X}_{2}} & S{{X}_{2}}+2{{S}_{1}}{{X}_{1}}+{{S}_{2}}X & t{{X}_{2}}+2{{t}_{1}}{{X}_{1}}+{{t}_{2}}X \\ \end{matrix} \right|\] \[=\left| \begin{matrix} X & 0 & 0 \\ {{X}_{1}} & {{S}_{1}}X & {{t}_{1}}X \\ {{X}_{2}} & 2{{S}_{1}}{{X}_{1}}+{{S}_{2}}X & 2{{t}_{1}}{{X}_{1}}+{{t}_{2}}X \\ \end{matrix} \right|\] (Applying \[{{C}_{2}}\to {{C}_{2}}-S{{C}_{1}}\] and \[{{C}_{3}}\to {{C}_{3}}-t{{C}_{1}}\]) \[={{X}^{2}}\left| \begin{matrix} {{S}_{1}} & {{t}_{1}} \\ 2{{S}_{1}}{{X}_{1}}+{{S}_{2}}X & 2{{t}_{1}}{{X}_{1}}+{{t}_{2}}X \\ \end{matrix} \right|\] \[={{X}^{3}}\left| \begin{matrix} {{S}_{1}} & {{t}_{1}} \\ {{S}_{2}} & {{t}_{2}} \\ \end{matrix} \right|\] (Applying \[{{R}_{2}}\to {{R}_{2}}-2{{X}_{1}}{{R}_{1}}\] ) \[\therefore \,\,\,\,\,\,n=3\]You need to login to perform this action.
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