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If the matrix ((a,2/3,2/3),(2/3,1/3,b),(...

If the matrix `((a,2/3,2/3),(2/3,1/3,b),(c,x,y))` is an orthogonal matrix, then `3a-6b=`

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Show the A=(1)/(3)[(-1,2,-2),(-2,1,2),(2,2,1)] is proper orthogonal matrix.

A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| . Also |A^T|=|A| and for any two square matrix A and B of same order \|AB|=|A||B| On the basis of above information answer the following question: If A=[(p,q,r),(q,r,p),(r,p,q)] be an orthogonal matrix and pqr=1, then p^3+q^3+r^3 may be equal to (A) 2 (B) 1 (C) 3 (D) -1

Knowledge Check

  • If A=(1)/(3) [(1,2,2),(2,1,-2),(a,2,b)] is an orthogonal matrix, then

    A
    a = – 2, b = – 1
    B
    a = 2, b = 1
    C
    a = 2, b = – 1
    D
    a = – 2, b = 1

  • If A=1/3{:[(1,2,2),(2,1,-2),(a,2,b)]:} is an orthogonal matrix, then

    A
    `a=2,b=1`
    B
    `a=-2,b=-1`
    C
    `a=2,b=-1`
    D
    `a=-2,b=1`

  • If A= (1)/(3) [ (1,2,2),(2,1,-2),(a,2,b)] is an orthogonal matrix then

    A
    a=1 , b=2
    B
    a=-2 , b=1
    C
    a=3 , b=- 1
    D
    a=- 2 , b =-1

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    Assertion (A) : If the matrix P = [(0,2b,-2),(3,1,3),(3a,3,3)] is a symmetric matrix, then a = (-2)/(3) and b = (3)/(2) Reason (R) : If P is a symmetric matric, then p' = - p

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