JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The value of \(k \in R\), for which the following system of linear equations \(3 x-y+4 z=3\) \(x+2 y-3 x=-2\) \(6 x+5 y+k z=-3\) has infinitely many solutions, is:
- A \(3\)
- B \(-3\)
- C \(5\)
- D \(-5\)
Answer & Solution
Correct Answer
(D) \(-5\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}3 & -1 & 4 \\ 1 & 2 & -3 \\ 6 & 5 & K\end{array}\right|=0\) \(\Rightarrow 3(2 \mathrm{~K}+15)+\mathrm{K}+18-28=0\) \(\Rightarrow 7 \mathrm{~K}+35=0 \Rightarrow \mathrm{K}-5\)
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