Matrices and Determinants 4 Question 31
32. For what value of $k$, does the following system of equations possess a non-trivial solution over the set of rationals $x+y-2 z=0,2 x-3 y+z=0$, and $x-5 y+4 z=k$
Find all the solutions.
$(1979,3 \mathrm{M})$
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Answer:
Correct Answer: 32. (9)
Solution:
- Since, the given system of equations posses non-trivial solution, if $\left|\begin{array}{ccc}0 & 1 & -2 \\ 0 & -3 & 1 \\ k & -5 & 4\end{array}\right|=0 \Rightarrow k=0$
On solving the equations $x=y=z=\lambda$
[say]
$\therefore$ For $k=0$, the system has infinite solutions of $\lambda \in R$.
