Given an orthogonal matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&1&1&1 \\ 1&1&{ - 1}&{ - 1} \\ 1&{ - 1}&0&0 \\ 0&0&1&{ - 1} \end{array}} \right],\,{\left[ {{\text{A}}{{\text{A}}^{\text{T}}}} \right]^{ - 1}}\,{\text{is}}\]
A. \[\left[ {\begin{array}{*{20}{c}} {\frac{1}{4}}&0&0&0 \\ 0&{\frac{1}{4}}&0&0 \\ 0&0&{\frac{1}{2}}&0 \\ 0&0&0&{\frac{1}{2}} \end{array}} \right]\]
B. \[\left[ {\begin{array}{*{20}{c}} {\frac{1}{2}}&0&0&0 \\ 0&{\frac{1}{2}}&0&0 \\ 0&0&{\frac{1}{2}}&0 \\ 0&0&0&{\frac{1}{2}} \end{array}} \right]\]
C. \[\left[ {\begin{array}{*{20}{c}} 1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \\ 0&0&0&1 \end{array}} \right]\]
D. \[\left[ {\begin{array}{*{20}{c}} {\frac{1}{4}}&0&0&0 \\ 0&{\frac{1}{4}}&0&0 \\ 0&0&{\frac{1}{4}}&0 \\ 0&0&0&{\frac{1}{4}} \end{array}} \right]\]
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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