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Engineering Maths · Q150

Linear Algebra

Engineering and GATE · Engineering Maths · question 150

Q150

Given an orthogonal matrix \[ A = [ array*20c 1&1&1&1 \\ 1&1& - 1& - 1 \\ 1& - 1&0&0 \\ 0&0&1& - 1 array ],\, [ A A^ T ]^ - 1\, is\]

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]
Answer
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

Solution

Answer: Option C
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