A) Three values of t
B) two values of t
C) One value of t
D) no value of t
Correct Answer: C
Solution :
Determinant of coefficients = |
\[\left| \begin{matrix} t & t+1 & t-1 \\ t+1 & t & t+2 \\ t-1 & t+2 & t \\ \end{matrix} \right|=\left| \begin{matrix} t & 1 & -1 \\ t+1 & -1 & 1 \\ t-1 & 3 & 1 \\ \end{matrix} \right|\] |
\[=\left| \begin{matrix} t & 1 & -1 \\ 2t+1 & 0 & 0 \\ 2t-1 & 4 & 0 \\ \end{matrix} \right|=-\,4(2t+1)\] |
For non-trivial solution \[t=-\frac{1}{2}.\] |
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