Q140
For the given orthogonal matrix Q\[ Q = [ array*20c 3/7&2/7&6/7 \\ - 6/7&3/7&2/7 \\ 2/7&6/7& - 3/7 array ]\] The inverse is
For the given orthogonal matrix Q
{\text{Q}} = \left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}} \\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}} \end{array}} \right]
The inverse is
{\text{Q}} = \left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}} \\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}} \end{array}} \right]
The inverse is
A.
\left[ {\begin{array}{*{20}{c}}
{\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}} \\
{ - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}} \\
{\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}}
\end{array}} \right]
B.
\left[ {\begin{array}{*{20}{c}}
{ - \frac{3}{7}}&{ - \frac{2}{7}}&{ - \frac{6}{7}} \\
{\frac{6}{7}}&{ - \frac{3}{7}}&{ - \frac{2}{7}} \\
{ - \frac{2}{7}}&{ - \frac{6}{7}}&{\frac{3}{7}}
\end{array}} \right]
C.
\left[ {\begin{array}{*{20}{c}}
{\frac{3}{7}}&{ - \frac{6}{7}}&{\frac{2}{7}} \\
{\frac{2}{7}}&{\frac{3}{7}}&{\frac{6}{7}} \\
{\frac{6}{7}}&{\frac{2}{7}}&{ - \frac{3}{7}}
\end{array}} \right]
AnswerD.
\left[ {\begin{array}{*{20}{c}}
{ - \frac{3}{7}}&{\frac{6}{7}}&{ - \frac{2}{7}} \\
{ - \frac{2}{7}}&{ - \frac{3}{7}}&{ - \frac{6}{7}} \\
{ - \frac{6}{7}}&{ - \frac{2}{7}}&{\frac{3}{7}}
\end{array}} \right]
Answer: Option C
Solution
Answer: Option C
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