Question
Download Solution PDFযদি \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\) , তাহলে A4 -এর মান কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFগণনা:
প্রদত্ত : \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\)
\({{\rm{A}}^2} = {\rm{AA}} = \left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\)
\(\Rightarrow {{\rm{A}}^2} = {\rm{\;}}\left[ {\begin{array}{*{20}{c}} {0 + 1}&{0 + 0}\\ {0 + 0}&{1 + 0} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\)
এখন,
\(\Rightarrow {{\rm{A}}^4} = {{\rm{A}}^2}{{\rm{A}}^2} = {\rm{\;}}\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right] = {\rm{\;}}\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\)
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