JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(S\) is the set of distinct values of \('b'\) for which the following system of linear equations \(x + y + z = 1;x + ay + z = 1;ax + by + z = 0\) has no solution , then \(S\) is :
- A a singleton
- B an empty set
- C an infinate set
- D a finate set contatining two or more elements
Answer & Solution
Correct Answer
(A) a singleton
Step-by-step Solution
Detailed explanation
\(D = \left| \begin{array}{l} 1\,\,\,1\,\,\,\,1\\ 1\,\,\,a\,\,\,1\\ 1\,\,\,b\,\,\,1 \end{array} \right|\, = 0\) \( \Rightarrow 1\left[ {a - b} \right]\, - 1\left[ {1 - a} \right] + 1\left[ {b - {a^2}} \right] = 0 \Rightarrow {\left( {a - 1} \right)^2} = 0\)…
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