JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The greatest value of \(c \in R\) for which the system of linear equations \(x - cy - cz = 0 \,\,;\,\, cx - y + cz = 0 \,\,;\,\, cx + cy - z = 0 \) has a non -trivial solution, is
- A \(-1\)
- B \(0.5\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(0.5\)
Step-by-step Solution
Detailed explanation
For non -trivial solution \(D = 0\) \(\left| {\begin{array}{*{20}{c}} 1&{ - c}&{ - c}\\ c&{ - 1}&c\\ c&c&{ - 1} \end{array}} \right| = 0 \Rightarrow 2{c^3} + 3{c^2} - 1 = 0\) \( \Rightarrow {\left( {c + 1} \right)^2}\left( {2c - 1} \right) = 0\) \(\therefore \) Greatest value of…
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