SOLUTION: Show that the set s={u,v,6u-8v}, is linearly dependent regardless of what vectors u and v are.

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Question 28247: Show that the set s={u,v,6u-8v}, is linearly dependent regardless of what vectors u and v are.
Answer by venugopalramana(3286) About Me  (Show Source):
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Show that the set s={u,v,6u-8v}, is linearly dependent regardless of what vectors u and v are.
WE HAVE TO SHOW THAT THERE ARE A SET OF VALUES A1,A2,A3 NOT ALL EQUAL TO ZERO SUCH THAT
A1U+A2V+A3(6U-8V)=0
WE CAN EASILY SEE THAT IF
A1=-6 AND A2=8 AND A3=1......WE GET
-6U+8V+6U-8V=0...HENCE
the set s={u,v,6u-8v}, is linearly dependent regardless of what vectors u and v are.