Question

What is the difference between linear dependence and linear independence?

Answer 1

one sounds parametric

Answer 2

linear dependence of vectors x1 through xn means there is a nontrivial solution to:

a1x1+a2x2+a3x3+...anxn=0 for vectors x1..xn, real numbers a1..an

Answer 3

independence of those vectors means there is only the trivial solution (all ai=0)

Answer 4

\[(x_1, x_1,..., x_n)\] linearly independent means if [\sum_{i=1}^n{a_ix_i}=0\] then each \[a_i=0\]

Answer 5

\[\sum_{i=1}^n{a_ix_i}=0\]

Answer 6

that is what i meant to write

Answer 7

bad latex on my part

Answer 8

hello polpak! i am here to watch amistre get to 1000. better that waiting for the ball to drop in time square

Answer 9

meh. ;p

Answer 10

:)