Question
Download Solution PDFआव्यूह
1. A के प्रतिलोम का अस्तित्व नहीं है
2. A3 = A
3. 3A = A2
उपर्युक्त में से कौन-से सही हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
आव्यूह गुणन:
- दो मैट्रिक्स को केवल तभी गुणा किया जा सकता है जब पहले मैट्रिक्स की कॉलम संख्या दूसरे मैट्रिक्स की पंक्ति संख्या के बराबर हो।
- यदि A एक व्युत्क्रमणीय आव्यूह नहीं है तो |A| = 0 है
- यदि A एक अव्युत्क्रमणीय आव्यूह है तो |A| = 0 है
गणना:
Given that,
|A| = 1(1 - 1) - 1(1 - 1) + 1 (1 - 1) = 0
इसलिए, A का व्युत्क्रम मौजूद नहीं है
⇒ A2 =
⇒ A2 =
⇒ A3 = A2 . A
⇒ A3 =
⇒ A3 =
⇒ A3 = 9
Hence, statement (2) is incorrect.
अब, 3A का मान है
= 3
⇒ 3A =
∴ 3A = A2
Hence, statement (3) is correct.
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