JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of equations \(-k x+3 y-14 z=25\) \(-15 x+4 y-k z=3\) \(-4 x+y+3 z=4\) is consistent for all \(k\) in the set
- A \(R\)
- B \(R -\{-11,13\}\)
- C \(R -\{13\}\)
- D \(R -\{-11,11\}\)
Answer & Solution
Correct Answer
(D) \(R -\{-11,11\}\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}- k & 3 & -14 \\ -15 & 4 & - k \\ -4 & 1 & 3\end{array}\right|=121- k ^{2}\) \(\Delta \neq 0 \quad k \in R -\{11,-11\} \quad\) (Unique sol.) If \(k =11\)…
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