JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(2x + 3y - z = 0\), \(x + ky - 2z = 0\) and \(2x - y + z = 0\) has a non -trivial solution \((x, y, z)\), then \(\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k\) is equal to
- A \(\frac{3}{4}\)
- B \(-4\)
- C \(\frac{1}{2}\)
- D \(-\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
system of equations has non trival solution \(\therefore D = 0 = \left| {\begin{array}{*{20}{c}} 2&3&{ - 1}\\ 1&k&{ - 2}\\ 2&{ - 1}&1 \end{array}} \right| = 0\) \( \Rightarrow k = \frac{9}{2}\) So equation are \(2x + 3y - z = 0\,\,\,\,\,\,\,\,\,.....\left( 1 \right)\)…
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