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On real numbers, (a*b=a+b+\lambda ab) is defined. If (\lambda\neq 0), which element will not have an inverse?वास्तविक संख्याओं पर (a*b=a+b+\lambda ab) परिभाषित है। यदि (\lambda\neq 0), तो किस अवयव का प्रतिलोम नहीं होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-\frac{1}{\lambda})(-\frac{1}{\lambda})
Step 1: The identity is (0). Step 2: (a*x=0\Rightarrow a+x+\lambda ax=0\Rightarrow x(1+\lambda a)=-a). If (1+\lambda a=0), no inverse is obtained. Step 3: Identify the value that makes the denominator zero.चरण 1: इस क्रिया का तत्समक (0) है। चरण 2: (a*x=0\Rightarrow a+x+\lambda ax=0\Rightarrow x(1+\lambda a)=-a)। यदि (1+\lambda a=0), तो प्रतिलोम नहीं मिलेगा। चरण 3: हर वाले पद को शून्य बनाने वाले मान को अलग पहचानें।
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