Question

which of the following sets of vectors in R^6 are linearly independent?
A. {(8 0 0 0 0 0),(0 7 0 0 0 0),(0 0 16 0 0 0)}
B. {(8 0 0 0 0 0),(7 0 0 0 0 0),(0 16 0 0 0 16)}
c. {(808080),(080808),(888888)}
D.{(088000),(000000),(16000016)}
E. {(008800),(070070),(16 0 0 0 016)}
F. {(800800),(070070),(0 0 16 0 0 16)}

Answer 1

if you can write any of the 3 in terms of the 2 other vectors they are not linearly independent.

Answer 2

B. $$(8,0,0,0,0,0)=\frac87(7,0,0,0,0,0)+0(0,16,0,0,0,16)$$so they're dependent.
C. $$(8,8,8,8,8,8)=(8,0,8,0,8,0)+(0,8,0,8,0,8)$$so they're dependent as well

Answer 3

the other ones you'll notice must be linearly independent because none of the 3 vectors share elements

Answer 4

i try it on webwork but it says incorrect =/

Answer 5

try AEF