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Math Help - Linear Independence

  1. #1
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    Linear Independence

    Suppose that  {v_1,v_2,......,v_n} is a linearly independent set of vectors in  R^n . Show that if A is an n x n nonsingular matrix, then  {Av_1,Av_2,......,Av_n} is linearly independent.
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  2. #2
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    Quote Originally Posted by TeeWorlves1234124 View Post
    Suppose that  {v_1,v_2,......,v_n} is a linearly independent set of vectors in  R^n . Show that if A is an n x n nonsingular matrix, then  {Av_1,Av_2,......,Av_n} is linearly independent.
    For scalars a_i, 0=\sum\limits_{i=1}^na_iAv_i=\sum\limits_{i=1}^nA(  a_iv_i)=A\left(\sum\limits_{i=1}^na_iv_i\right).

    Now use that A is non-singular and then use that the given vectors are lin. indep.

    Tonio
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