यदि और |2A| = k है, तो k का मान ज्ञात कीजिए। 

  1. 2765
  2. 2576
  3. 2912
  4. इनमें से कोई नहीं 

Answer (Detailed Solution Below)

Option 3 : 2912
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Detailed Solution

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संकल्पना:

  • यदि  कोटि 2 वाली एक वर्ग आव्यूह है, तो A की सारणिक को |A| = a11 × {(a22 × a33) – (a23 × a32)} - a12 × {(a21 × a33) – (a23 × a31)} + a13 × {(a21 × a32) – (a22 × a31)} द्वारा ज्ञात किया जाता है।  
  • यदि A आव्यूह n वाली एक आव्यूह है, तो |k ⋅ A| = kn ⋅ |A| है, जहाँ k ∈ R है। 

गणना:

दिया गया है:  और |2A| = k

⇒ |A| = 3 × (30 - 63) - 4 × (55 - 56) + 9 × (99 - 48)

⇒ |A| = - 99 + 4 + 459 = 364

चूँकि हम जानते हैं कि, यदि A आव्यूह n वाली एक आव्यूह है, तो |k ⋅ A| = kn ⋅ |A| है, जहाँ k ∈ R है। 

⇒ |2A| = 23 ⋅ 364 = 2912

अतः सही विकल्प 3 है।

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