Question

Prove that W (a,2a,3a) is a subset of R^3

Answer 1

subsets are closed under addition and scalar multiplication, and also contain the 0 vector

Answer 2

Can you prove that?

Answer 3

not with out knowing a little more about the question. What assumptions are to be made?

Answer 4

if a is a vector in W, and the matrix A is formed by multiples of a, then its not a linearly independant basis

Answer 5

is "a" composed of more than 4 components? or is it a 3x1 column vector? (or a 1x3 row vector)?

Answer 6

(a,2a,3a) the a's are just to show that the second component is 2x the first, and the third component is 3x the first

Answer 7

yes, and multiples of the same vector are not linearly dependant ... they are all the same vector