JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of linear equations \(2 x+y-z=3\) \(x-y-z=\alpha\) \(3 x+3 y+\beta z=3\) has infinitely many solution, then \(\alpha+\beta-\alpha \beta\) is equal to .... .
- A \(1\)
- B \(2\)
- C \(3\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(2 \times(\mathrm{i})-(\mathrm{ii})-(\mathrm{iii}) \text { gives : }\) \(-(1+\beta) \mathrm{z}=3-\alpha\) For infinitely many solution \(\beta+1=0=3-\alpha \Rightarrow(\alpha, \beta)=(3,-1)\) Hence, \(\alpha+\beta-\alpha \beta=5\)
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