Question 28247
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.