If A=131     2       22     1    −2a      2      b is an orthogonal matrix, then

If A=131     2       22     1    2a      2      b is an orthogonal matrix, then

  1. A

    a 2,b =1

  2. B

    a =-2,b = -1

  3. C

    a= 2, b =-1

  4. D

    a =- 2, b =1

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    Solution:

    Since A is an orthogonal matrix. 

     AAT=1 13122212a2b1312a21222b=100010001 19122212a2b12a21222b=100010001 90a+4+2b092a+22ba+4+2b2a+22ba2+4+b2=900090009a+4+2b=0,2a+22b=0 and a2+4+b2=9a+2b+4=0,ab+1=0 and a2+b2=5

     a=2,b=1

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