JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of linear equations \(3 x-2 y-k z=10\); \(2 x-4 y-2 z=6\) ; \(x+2 y-z=5\, m\) is inconsistent if
- A \(k =3, m =\frac{4}{5}\)
- B \(k \neq 3, m \in R\)
- C \(k \neq 3, m \neq \frac{4}{5}\)
- D \(k =3, m \neq \frac{4}{5}\)
Answer & Solution
Correct Answer
(D) \(k =3, m \neq \frac{4}{5}\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}3 & -2 & -k \\ 2 & -4 & -2 \\ 1 & 2 & -1\end{array}\right|=0\) \(\Rightarrow \quad 24-2(0)- k (8)=0 \Rightarrow k =3\) \(\Delta_{ x }=\left|\begin{array}{ccc}10 & -2 & -3 \\ 6 & -4 & -2 \\ 5 m & 2 & -1\end{array}\right|\)…
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