Question

Can anyone help explain to the concept of spanning sets in linear algebra?

Answer 1

yes every vector in the set can be wriiten as a linear combination of all the vectors in the span

Answer 2

for example the vector (1, 5, 3 ) can be written in R3 as 1(1,0,0) + 5(0,1,0) + 3 (0,0,1) in fact every vector in R3 can be written as a(1,0,0) +b(0,1,0) + c(0,0,1).
a, ,b, c are all reals

Answer 3

Thanks, that makes sense, kind of hard to grasp for me for some reason

Answer 4

another question, how would you know if a span of S in Rn does not have a solution or would all spans in Rn have a solution?