आव्यूह \(\rm \begin{bmatrix} 3 & 0 & 0\\ 0 & 4 & 0\\ 0 & 0 & 0 \end{bmatrix}\) एक ______ है।

  1. पहचान आव्यूह
  2. सममित आव्यूह
  3. विषम सममित आव्यूह
  4. इनमें से कोई नहीं

Answer (Detailed Solution Below)

Option 2 : सममित आव्यूह
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Detailed Solution

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अवधारणा:

एक वर्ग आव्यूह A = [aij]n × n को सममित कहा जाता है यदि  AT = A

T (परिवर्त) पंक्तियों को स्तम्भ और स्तम्भ को पंक्तियों में बदलकर प्राप्त किया जाता है

गणना:

माना A = \(\rm \begin{bmatrix} 3 & 0 & 0\\ 0 & 4 & 0\\ 0 & 0 & 0 \end{bmatrix}\)

 AT = \(\rm \begin{bmatrix} 3 & 0 & 0\\ 0 & 4 & 0\\ 0 & 0 & 0 \end{bmatrix}\)   = A

A एक सममित आव्यूह है

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