Question

The numbers of real values of t such that the system of homogeneous equations
tx + (t + 1)y + (t - 1)z = 0
(t + 1)x + ty + (t + 2)z = 0
(t - 1)x + (t + 2)y + tz = 0
has non-trivial solutions, is

• A. 3
• B. 2
• C. 1
• D. 4

Answer 1

Answer: (C)

1

For non trivial soln $△=0$

$\left|\begin{array}{ccc}t& t+1& t-1\\ t+1& t& t+2\\ t-1& t+2& t\end{array}\right|=0$

$\Rightarrow \left|\begin{array}{ccc}t& t+1& t-1\\ 1& -1& 3\\ -1& 1& 1\end{array}\right|=0$

$\begin{array}{c}{c}_2\to c_2-c_1\\ c_3\to c_3-c_1\end{array}$

$-8t-4=0$

$\Rightarrow t=\frac{-1}{2}$

So, for only one real value of $t$ exists.