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Question
Which of the following is as orthogonal matrix?
Which of the following is as orthogonal matrix?
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Solution
The correct option is A ⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦
For A=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦
AT=⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦
Thus
AAT=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=I
Hence A is an orthogonal matrix.
For A=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦
AT=⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦
Thus
AAT=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=I
Hence A is an orthogonal matrix.
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