Is column space a vector space?

The column space is all the possible vectors you can create by taking linear combinations of the given matrix. In the same way that a linear equation is not the same as a line, a column space is similar to the span, but not the same. The column space is the matrix version of a span.Click to see full answer. In this manner, is column space a subspace?In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The row and column spaces are subspaces of the real spaces Rn and Rm respectively.Subsequently, question is, how do you define a vector space? Definition: A vector space is a set V on which two operations + and · are defined, called vector addition and scalar multiplication. The operation + (vector addition) must satisfy the following conditions: Closure: If u and v are any vectors in V, then the sum u + v belongs to V. Keeping this in consideration, how many vectors are in Col A? Note the basis for col A consists of exactly 3 vectors.Is W in v1 v2 v3?{v1,v2,v3} is a set containing only three vectors v1, v2, v3. Apparently, w equals none of these three, so w /∈ {v1,v2,v3}. (b) span{v1,v2,v3} is the set containing ALL possible linear combinations of v1, v2, v3. Particularly, any scalar multiple of v1, say, 2v1,3v1,4v1,···, are all in the span.