Question

What do you mean by linearly independent vectors ?

Answer 1

they can not be written as a sum of other vectors

Answer 2

http://en.wikipedia.org/wiki/Linear_independence
A subset S of a vector space V is called linearly dependent if there exist a finite number of distinct vectors v1, v2, ..., vn in S and scalars a1, a2, ..., an, not all zero, such that

a_1 v_1 + a_2 v_2 + \cdots + a_n v_n = 0.
Note that the zero on the right is the zero vector, not the number zero.

For any vectors u1, u2, ..., un we have that

0 u_1 + 0 u_2 + \cdots + 0 u_n = 0,
This is called the trivial representation of 0 as a linear combination of u1, u2, ..., un, this motivates a very simple definition of both linear independence and linear dependence, for a set to be linearly dependent, there must exist a non-trivial representation of 0 as a linear combination of vectors in the set.

A subset S of a vector space V is then said to be linearly independent if it is not linearly dependent, in other words, a set is linearly independent if the only representations of 0 as a linear combination of its vectors are trivial representations.[1]

Answer 3

There is no other linear combinaton of vectors that will produce the independent vector

Answer 4

yeah

Answer 5

it is like half of linear algebra class. lol i am guessing you are taking linear algebra

Answer 6

example, i,j,k, 3 linearly independent vactors that span and form the basis for 3-space

Answer 7

Thank you very much !
Happy new year!

Answer 8

holy crap it is 5 minutes away... BYE

Answer 9

happy new year

Answer 10

it is easier to understand lin. independent vectors by finding a set that are not lin. independent .

Answer 11

the vectors in the set { (1,1) , (2,2) (3,4) } are not linearly independent , because (1,1) can be written as a linear combination of (2,2) and (3,4) .
but the set of vectors { (1,1) (3,4) } are linearly independent.