यदि A = \(\begin{bmatrix} -3 & 4\\ 0 & 1 \end{bmatrix}\) है, तो A - AT किसके बराबर है? 

  1. \(\begin{bmatrix} 0 &-4 \\ -4&0 \end{bmatrix}\)
  2. \(\begin{bmatrix} 0 &4 \\ 4&0 \end{bmatrix}\)
  3. \(\begin{bmatrix} 0 &4 \\ -4&0 \end{bmatrix}\)
  4. \(\begin{bmatrix} 0 &-4 \\ 4&0 \end{bmatrix}\)

Answer (Detailed Solution Below)

Option 3 : \(\begin{bmatrix} 0 &4 \\ -4&0 \end{bmatrix}\)
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संकल्पना:

एक आव्यूह का पक्षांतर:

वास्तविक आव्यूह के पंक्तियों और स्तंभों को एक-दूसरे से परिवर्तित करके प्राप्त नए आव्यूह को आव्यूह का पक्षांतर कहा जाता है। 

इसे A′ या Aद्वारा दर्शाया गया है। 

 

गणना:

दिया गया है:

A = \(\begin{bmatrix} -3 & 4\\ 0 & 1 \end{bmatrix}\)

अब आव्यूह A का पक्षांतर ज्ञात करने के लिए,

AT = \(\begin{bmatrix} -3 & 0\\ 4 & 1 \end{bmatrix}\)

अब,

A - AT = \(\begin{bmatrix} -3 & 4\\ 0 & 1 \end{bmatrix}-\begin{bmatrix} -3 & 0\\ 4 & 1 \end{bmatrix}\)

\(= \begin{bmatrix} 0 &4 \\ -4&0 \end{bmatrix}\)

 

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