JEE MAIN - Mathematics (2021 - 20th July Evening Shift - No. 13)
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 :
3x $$-$$ y + 4z = 3,
x + 2y $$-$$ 3z = $$-$$2
6x + 5y + kz = $$-$$3,
has infinitely many solutions, is :
3
$$-$$5
5
$$-$$3
Explanation
$$\left| {\matrix{
3 & { - 1} & 4 \cr
1 & 2 & { - 3} \cr
6 & 5 & k \cr
} } \right| = 0$$
$$\Rightarrow$$ 3(2k + 15) + K + 18 $$-$$ 28 = 0
$$\Rightarrow$$ 7k + 35 = 0
$$\Rightarrow$$ k = $$-$$ 5
$$\Rightarrow$$ 3(2k + 15) + K + 18 $$-$$ 28 = 0
$$\Rightarrow$$ 7k + 35 = 0
$$\Rightarrow$$ k = $$-$$ 5
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