Question
Download Solution PDFयदि आव्यूह A = \(\left[ {\begin{array}{*{20}{c}} 0&1&{ - 1} \\ 4&{ - 3}&4 \\ 3&{ - 3}&4 \end{array}} \right]\) = B + C, जहाँ B सममित और C विषम सममित आव्यूह है , तो आव्यूह B ज्ञात कीजिए
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है, आव्यूह A = \(\left[ {\begin{array}{*{20}{c}} 0&1&{ - 1} \\ 4&{ - 3}&4 \\ 3&{ - 3}&4 \end{array}} \right]\)
A = B + C
यहाँ आव्यूह A को सममित और विषम सममित आव्यूह के योग के रूप में व्यक्त किया गया है।
तब, \(B=\frac{1}{2}(A+A^{T}) \ और \ C=\frac{1}{2}(A-A^{T})\)
जहाँ B सममित है और C विषम सममित आव्यूह है।
ज्ञात करें: आव्यूह B
A = \(\left[ {\begin{array}{*{20}{c}} 0&1&{ - 1} \\ 4&{ - 3}&4 \\ 3&{ - 3}&4 \end{array}} \right]\)
\(A^{T}=\begin{bmatrix} 0 & 4& 3 \\ 1 & -3 & -3 \\ -1& 4& 4 \\ \end{bmatrix}\)
\(A+ A^{T}=\left[ {\begin{array}{*{20}{c}} 0&1&{ - 1} \\ 4&{ - 3}&4 \\ 3&{ - 3}&4 \end{array}} \right] +\begin{bmatrix} 0 & 4& 3 \\ 1 & -3 & -3 \\ -1& 4& 4 \\ \end{bmatrix}\)
\(A+ A^{T}=\begin{bmatrix} 0 &5 & 2 \\ 5& -6 & 1 \\ 2& 1 & 8 \\ \end{bmatrix}\)
\(B=\frac{1}{2}(A+ A^{T})=\frac{1}{2}\begin{bmatrix} 0 &5 & 2 \\ 5& -6 & 1 \\ 2& 1 & 8 \\ \end{bmatrix}\)
Last updated on May 26, 2025
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