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[SOLVED] Q01 are linearly independent vectors, so are....

karush

Well-known member
Jan 31, 2012
3,066
Let A be invertible. Show that, if $\textbf{$v_i,v_2,v_j$}$ are linearly independent vectors, so are \textbf{$Av_1,Av_2,Av_3$}

definition


p57.png

ok I think this is the the definition we need for this practice exam question,
However I tried to insert using a link but not successful
I thot if we use a link the image would always be there unless we delete its source

as to the question... not real sure of the answer since one $c_n$ may equal 0 and another may not

Anyway Mahalo...
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
821
Yes, that is the definition of "linearly independent" you need. Now, what are you trying to prove?

You have "Show that, if $v_1$, $v_2$, $v_3$ are linearly independent, then so are $Av_1$, $Av_2$, $Av_3$" but what is "A"? If it is a general linear transformation this is not true. If A is an INVERTIBLE linear transformation then it is true and can be shown by applying $A^{-1}$ to both sides of$x_1Av_1+ x_2Av_2+ x_3Av_3= 0$.