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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(x+ ay+z\,= 3\) ; \(x + 2y+ 2z\, = 6\) ; \(x+5y+ 3z\, = b\) has no solution, then
- A \(a\, = 1\) , \(b\,\ne 9\)
- B \(a\,\ne - 1\) , \(b\, = 9\)
- C \(a\, = - 1\) , \(b = 9\)
- D \(a\, = -1\) , \(b\,\ne 9\)
Answer & Solution
Correct Answer
(D) \(a\, = -1\) , \(b\,\ne 9\)
Step-by-step Solution
Detailed explanation
As the system of equation has no solution then \(\Delta \) should be zero and at lest one of \({\Delta _1},{\Delta _2}\) and \({\Delta _3}\) should not be zero. \(\therefore \Delta = \begin{array}{*{20}{c}} 1&a&1\\ 1&2&2\\ 1&5&3 \end{array} = 0\)…
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