JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
An ordered pair \((\alpha , \beta )\) for which the system of linear equations \(\left( {1 + \alpha } \right)x + \beta y + z = 2\) ; \(\alpha x + \left( {1 + \beta } \right)y + z = 3\) ; \(\alpha x + \beta y + 2z = 2\) has a unique solution, is
- A \((2, 4)\)
- B \((-3, 1)\)
- C \((-4, 2)\)
- D \((1, -3)\)
Answer & Solution
Correct Answer
(A) \((2, 4)\)
Step-by-step Solution
Detailed explanation
\(\left( {1 + \alpha } \right)x + \beta y + z = 0\) \(\alpha x + \left( {1 + \beta } \right)y + z = 0\) \(\alpha x + \beta y + 2z = 0\) \(D = \left| {\begin{array}{*{20}{c}} {1 + \alpha }&\beta &1\\ \alpha &{1 + \beta }&1\\ \alpha &\beta &2 \end{array}} \right|\)…
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