JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \([\lambda]\) be the greatest integer less than or equal to \(\lambda\). The set of all values of \(\lambda\) for which the system of linear equations \(x+y+z=4,3 x+2 y+5 z=3\) \(9 x+4 y+(28+[\lambda]) z=[\lambda]\) has a solution is:
- A \({R}\)
- B \((-\infty,-9) \cup(-9, \infty)\)
- C \([-9,-8)\)
- D \((-\infty,-9) \cup[-8, \infty)\)
Answer & Solution
Correct Answer
(A) \({R}\)
Step-by-step Solution
Detailed explanation
\(\left| {\begin{array}{*{20}{r}} 1&1&1\\ 3&2&2\\ 9&4&{28 + [\lambda ]} \end{array}} \right|\) \(=-24-[\lambda] +15=-[\lambda]-9\) if \([\lambda]+9 \neq 0\) then unique solution if \([\lambda]+9=0\) then \(\mathrm{D}_{1}=\mathrm{D}_{2}=\mathrm{D}_{3}=0\) so infinite solutions…
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