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:

  1. 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 $\lambda \in R$.



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