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Math Help - Linear Transformations

  1. #1
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    Linear Transformations

    I need help understanding linear tranformations. The question asks:

    Which of the following transformations are linear?

    A. y1 = 8, y2 = 7, y3 = 2
    B. y1 = 6x1, y2 = 5
    C. y1 = -10x1, y2 = 9x1, y3 = 4x1
    D. y1 = 0, y2 = 7x1
    E. y1 = 0, y2 = x1x2
    F. y1 = 8x1 + x2, y2 = -x1

    What am I supposed to do here?


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  2. #2
    MHF Contributor

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    Quote Originally Posted by My Little Pony View Post
    I need help understanding linear tranformations. The question asks:

    Which of the following transformations are linear?

    A. y1 = 8, y2 = 7, y3 = 2
    B. y1 = 6x1, y2 = 5
    C. y1 = -10x1, y2 = 9x1, y3 = 4x1
    D. y1 = 0, y2 = 7x1
    E. y1 = 0, y2 = x1x2
    F. y1 = 8x1 + x2, y2 = -x1

    What am I supposed to do here?


    A transformation, T, is "linear" if and only if T(u+ v)= T(u)+ T(v) and T(av)= aT(v) for u and v vectors and a a number.

    For example, for A, T(x1,x2,x3)= (8, 7, 2) no matter what "x1", "x2", or "x3" are. So T(ax1, ax2, ax3)= (8, 7, 2) also. Is that the same as aT(x1,x2,x3)?

    For B, T(x1)= (6x1, 5) so T(ax1)= (6ax1, 5). Is that the same as aT(x1)?
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