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Math Help - Show that multiplication by A maps every point in the plane onto the line.

  1. #1
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    Show that multiplication by A maps every point in the plane onto the line.

    Show that multiplication by A = \begin{bmatrix}3 & 1\\ 6 & 2\end{bmatrix}
    maps every point in the plane onto the line y = 2x.

    I tried to see what happens with the unit square and the points in the unit square is easy to see that they maps onto the line y = 2x. But does that equals that every point in the plane maps onto the line?

    /regards
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  2. #2
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    Tejas
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    Re: Show that multiplication by A maps every point in the plane onto the line.

    well, no, but: what can you say if A maps every basis element of a basis for \mathbb{R}^2 onto the line y = 2x?

    conversely, given a point (t,2t) on the line, can you find some element (x,y) with A(x,y) = (t,2t)?
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