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Math Help - Matrix and Linear Mapping

  1. #1
    Senior Member slevvio's Avatar
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    Matrix and Linear Mapping

     h: {\mathbb{R} }^3 \rightarrow {\mathbb{R} }^2 is given by  h(x,y,z) =(7x, y-z) is a linear mapping.

    For this function, write down its matrix with respect to the standard bases of the domain and codomain.

    I took this to mean  h_A (\bold{x} ) = A \bold{x} = A \begin{bmatrix} x\\ y \\ z \\ \end{bmatrix} = \begin{bmatrix} 7x \\ y-z\\ \end {bmatrix}

    where  A = \begin{bmatrix} 7 & 0 & 0 \\ 0 & 1 & -1 \\ \end{bmatrix} . But how do I write this down with respect to the standard bases of the domain and codomain. I know these are (1,0,0), (0,1,0), (0,0,1) , (1,0), (0,1). Thanks very much.
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  2. #2
    Junior Member
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    hehe, I think you alrady did write it with respect to the standard basis, since

    h(1,0,0)=(7,0); h(0,1,0)=(0,1); h(0,0,1)=(0,-1)

    and that`s, by definition, hoy you find the associate matrix of a linear transformation: "hanging" the vectors which result of finding the images of the standard basis by the transformation.
    So A itself is the matrix you are looking for...

    I hope that will be useful.
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  3. #3
    Senior Member slevvio's Avatar
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    ok thank you, I usually know what to do in questions like this but the lingo confuses me hehe
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