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If P is a 3xx3 matrix such that P^T = 2P...

If P is a `3xx3` matrix such that `P^T = 2P+I`, where `P^T` is the transpose of P and I is the `3xx3` identity matrix, then there exists a column matrix, `X = [[x],[y],[z]]!=[[0],[0],[0]]` such that

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Knowledge Check

  • If P is a 3xx3 matrix such that P^(T) = 2P +I, where P^(T) is the transpose f P and I is the 3xx3 identify matrix then there exists a column matrix X = [(x),(y),(z)] != [ (0),(0),(0)] such that :

    A
    `PX = [(0),(0),(0)] `
    B
    PX = X
    C
    PX = 2X
    D
    PX = - X

  • If P is a 3xx3 matrix such that P^(T)=2P+I whre P^(T) is the transpose of P and I is the 3xx3 identify matrix, then thre exists a column matrix X=[(x),(y),(z)]!=[(0),(0),(0)] such that

    A
    `PX=[(0),(0),(0)]`
    B
    `PX=X`
    C
    `PX=2X`
    D
    `PX=-X`

  • P is a 2xx2 matrix . P'=P^(-1) then P=……..

    A
    `[{:(costheta,-sintheta),(-sintheta,costheta):}]`
    B
    `[{:(costheta,sintheta),(-sintheta,costheta):}]`
    C
    `[{:(-costheta,sintheta),(sintheta,-costheta):}]`
    D
    None of these

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