I am to find the image of the set S under the given transformation, but I do know how to start.?

NetherCraft 0

S = {(u,v) = | 0<= u <=3, 0<= v<=2}

with x = 2u +3v , y = u – v

1 Answer

  • You sort of have 4 points to make your image. You of course have more than that, but the maximum and minimum values of u and v are the best choices.

    Sketch your graph and plot x and y when u = 0 and v = 0. For this point you just get the origin.

    Do the same thing for x and y when u = 3 and v = 0. You’ll get the point (6, 3).

    Plot x and y for u = 0 and v = 2 you’ll get the point (6, -2).

    Once again for u = 3 and v = 2. You’ll get the point (12, 1).

    Connect the dots and shade the region you get and S is any point in the region.

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