JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(2 x + y - z =7\) ; \(x-3 y+2 z=1\) ; \(x +4 y +\delta z = k\), where \(\delta, k \in R\) has infinitely many solutions, then \(\delta+ k\) is equal to
- A \(-3\)
- B \(3\)
- C \(6\)
- D \(9\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(\quad\left|\begin{array}{ccc}2 & 1 & -1 \\ 1 & -3 & 2 \\ 1 & 4 & \delta\end{array}\right|=0\) \(\Rightarrow \delta=-3\) And \(\left|\begin{array}{ccr}7 & 1 & -1 \\ 1 & -3 & 2 \\ K & 4 & -3\end{array}\right|=0 \Rightarrow K =6\) \(\Rightarrow \delta+ K =3\) Alternate…
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