Matrices And Determinants Ques 107
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.
$(1979,3 \mathrm{M})$
Show Answer
Answer:
Correct Answer: 107.$k=0$, the system has infinite many solutions
Solution:
Formula:
System of equations with 3 variables:
Since the given system of equations possesses a non-trivial solution, if $\left|\begin{array}{ccc}0 & 1 & -2 \\ 0 & -3 & 1 \\ k & -5 & 4\end{array}\right|=0 \Rightarrow k=1$
On solving the equations $x=y=z=\lambda$
[say]
$\therefore$ For $k=0$, the system has infinite solutions of $\lambda \in R$.
BETA
