i need help describing a column space. i don't really understand that.

Ex. Let A= (1,2,2,3),(1,4,2,5),(1,5,2,6)
How would you describe the column space for that?

Question

i need help describing a column space. i don't really understand that. 

Ex. Let A= (1,2,2,3),(1,4,2,5),(1,5,2,6) 
How would you describe the column space for that?

anonymous · Answer

if we have a system of linear equation $$Ax = b$$
then the column space of A will be the all RHS "b" that we can get by varying the x.

anonymous · Answer

I think the column space is the span of all the vectors in the matrix - but more importantly, it is the span of all the linearly independent vectors in your matrix . So i this example, you would find the rref(A) and the columns that don't have leading 1s in the rref, the corresponding columns in your original matrix, would be the basis of your column space and the span of these columns would be the column space. In your example, it will be the span of the first two columns.

anonymous · Answer

So, it means that column space are the 'space' (or set) that consist of all the linear combinations of the column of the matrix e.g 1 of first column + 3 of second column + 0 of third column and other combinations that are possible?