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
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. \[\left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{ - \frac{6}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{3}{7}}&{\frac{6}{7}} \\ {\frac{6}{7}}&{\frac{2}{7}}&{ - \frac{3}{7}} \end{array}} \right]\]
D. \[\left[ {\begin{array}{*{20}{c}} { - \frac{3}{7}}&{\frac{6}{7}}&{ - \frac{2}{7}} \\ { - \frac{2}{7}}&{ - \frac{3}{7}}&{ - \frac{6}{7}} \\ { - \frac{6}{7}}&{ - \frac{2}{7}}&{\frac{3}{7}} \end{array}} \right]\]
Answer: Option C
This Question Belongs to Engineering Maths >> Linear Algebra
A. 3, 3 + 5j, 6 - j
B. -6 + 5j, 3 + j, 3 - j
C. 3 + j, 3 - j, 5 + j
D. 3, -1 + 3j, -1 - 3j
A. 1024 and -1024
B. 1024√2 and -1024√2
C. 4√2 and -4√2
D. 512√2 and -512√2
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