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Math Help - Linear transformation

  1. #1
    Senior Member
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    Linear transformation

    Can someone check my answer

    Show that this is not a linear transformation

    T(\mathbf{x})=\begin{pmatrix}x_1^2\\x_2^2\end{pmat  rix}

    Check scalar multiplication condition

    T(\lambda \mathbf{x})=\begin{pmatrix}\lambda ^2 x_1^2\\\lambda ^2 x_2^2\end{pmatrix}

    =\lambda ^2\begin{pmatrix}x_1^2\\x_2^2\end{pmatrix}

    \neq \lambda\begin{pmatrix}x_1^2\\x_2^2\end{pmatrix} \ \forall\lambda
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  2. #2
    A Plied Mathematician
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    Just append \lambda T(\mathbf{x}) at the end there, and you'll have it.
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