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Q.21. Find the value of θ   i n   0 ,   2 π such that the matrix  2 sin θ - 1 sin θ cos θ sin θ + π 2 cos θ - 3 tan θ cos θ - π tan π - θ 0 is a skew symmetric matrix.

Dear Student,

As the given matrix is a skew symmetric matrix , then , a skew symmetric matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition      AT = A. or aji=-aijSo, a21=-a12 , a31=-a13  and a32=-a23Now, a21=-a12sinθ+π=-sin θsinθ cosπ+sinπ cosθ=-sinθ            sina+b=sina cosb+cosa sinbsinθ-1+0. cosθ=-sinθ                   sinπ=0 , cosπ=-1-sinθ+0=-sinθ-sinθ=-sinθ value of θ is 0 Now we can do similar with  a31=-a13cosθ-π=-cosθcosθcosπ+sinθsinπ=-cosθ            cosa-b=cosa cosb+sina sinbcosθ-1+sinθ.0=-cosθ              -cosθ+0=-cosθ-cosθ=-cosθvalue of θ is 0simillarlya32=-a23tanπ-θ=-tanθtanπ-tanθ1+tanπtanθ=-tanθ                          tana-b=tana-tanb1+tana tanb , tanπ=00-tanθ1+0.tanθ=-tanθ-tanθ=-tanθHence value of θ is 0

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