Question
Download Solution PDFयदि A = \(\begin{bmatrix} 4 & -3\\ 1 & 0 \end{bmatrix}\) है, तो A + AT का किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
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 AT द्वारा दर्शाया जाता है।
गणना:
दिया गया है:
A = \(\begin{bmatrix} 4 & -3\\ 1 & 0 \end{bmatrix}\)
अब आव्यूह A का पक्षांतर ज्ञात करने के लिए,
AT = \(\begin{bmatrix} 4 & 1\\ -3 & 0 \end{bmatrix} \)
अब,
A + AT = \(\begin{bmatrix} 4 & -3\\ 1 & 0 \end{bmatrix}+ \begin{bmatrix} 4 & 1\\ -3 & 0 \end{bmatrix}\)
\(= \begin{bmatrix} 4+4 &-3+1 \\ 1+(-3)&0+0 \end{bmatrix}\)
\(= \begin{bmatrix} 8 & -2\\ -2 & 0 \end{bmatrix} \)
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