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Thread: Linear dependent vectors

  1. September 24th 2009, 12:53 PM #1
    noles2188
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    Linear dependent vectors

    Consider a linear transformation T from R^n to R^p and some linearly dependent vectors v1, v2, ..., vm in R^n. Are the vectors T(v1), T(v2), ..., T(vm) necessarily linearly dependent? How can you tell?
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  2. September 24th 2009, 04:36 PM #2
    Jose27
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    Quote Originally Posted by noles2188 View Post
    Consider a linear transformation T from R^n to R^p and some linearly dependent vectors v1, v2, ..., vm in R^n. Are the vectors T(v1), T(v2), ..., T(vm) necessarily linearly dependent? How can you tell?
    Yes. Let v_m= a_1v_1 + ...+a_{m-1}v_{m-1} then T(v_m)=a_1T(v_1)+...+a_{m-1}T(v_{m-1}) which shows T(v_i) are linerly dependent
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