JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S\) be the set of all real values of \(k\) for which the system oflinear equations \(x +y + z = 2\) ; \(2x +y - z = 3\) ; \(3x + 2y + kz = 4\) has a unique solution. Then \(S\) is
- A an empty set
- B equal to \(R- \{0\}\)
- C equal to \(\{0\}\)
- D equal to \(R\)
Answer & Solution
Correct Answer
(B) equal to \(R- \{0\}\)
Step-by-step Solution
Detailed explanation
The system of linear equations is: \(x+y+z=2\) \(2x+y-z=3\) \(3x+2y+kz=4\) As, system as unique solution. So, \(\begin{array}{*{20}{c}} 1&1&1\\ 2&1&{ - 1}\\ 3&2&k \end{array} \ne 0\) \( \Rightarrow k + 2 - \left( {2k + 3} \right) + 1 \ne 0\) \( \Rightarrow k \ne 0\) Hence,…
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