Show whether the function is a linear operator from R2 to R2?

NetherCraft 0

T<x,y> = <x+y,2xy>

1 Answer

  • This function is not a linear operator. Linear opeartor must satisfy condition F(a+b) = F(a) + F(b).

    If we choose a=(1,0), b=(0,1), then

    T(a) = (1,0)

    T(b) = (1,0)

    T(a+b) = T(1,1) = (2,2)

    T(a) + T(b) = (1,0) + (1,0) = (2,0)

    We see that T(a+b) is not equal to T(a)+T(b).

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