Work out basis and dimension instantly with clear inputs, formula shown and shareable results.
A basis is a smallest spanning set. Placing the vectors as columns and row reducing finds which are independent; the pivot positions pick out a basis and their count is the dimension.
Dimension
dim(span) = rank of the matrix whose columns are the vectors
The second is twice the first, so the span has dimension 2 with one redundant vector.
Yes, infinitely many, but every basis of a given space has exactly the same number of vectors.