1. ## 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.

2. Originally Posted by TeeWorlves1234124
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