A) 100
B) 50
C) 200
D) None of these
Correct Answer: C
Solution :
[c] Consider \[{{A}^{2}}=\left[ \begin{matrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{matrix} \right]\left[ \begin{matrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]=I\,\,So\,\,{{A}^{3}}=\left[ \begin{matrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{matrix} \right]\] and So on \[tr(A)+tr({{A}^{2}})tr({{A}^{3}})+...+tr({{A}^{100}})\] \[=(-1)+(3)+(-1)+(3)+...+(-1)+(3)=200\]
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