The value of k $$\in$$R, for which the following system of linear equations 3x $$-$$ y + 4z = 3, x + 2y $$-$$ 3z = $$-$$2 6x + 5y + kz = $$-$$3, has infinitely many solutions, is :
JEE · Math · previous-year question
- A.3
- B.$$-$$5correct
- C.5
- D.$$-$$3
Answer
B. $$-$$5
Explanation
$$\left| {\begin{matrix} 3 & { - 1} & 4 \\ 1 & 2 & { - 3} \\ 6 & 5 & k \\ \end{matrix} } \right| = 0$$ $$\Rightarrow$$ 3(2k + 15) + K + 18 $$-$$ 28 = 0 $$\Rightarrow$$ 7k + 35 = 0 $$\Rightarrow$$ k = $$-$$ 5
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