Question

What does basis mean? For example.
"The pivot column of a matrix A form a basis for Col A"

Answer 1

I know what pivot columns are so I can find the basis for Col A of matrix A but what does that represent? Is there something special about this?

Answer 2

Maybe it should say : "The pivot COLUMNS (plural) of a matrix A form a basis for Col A"

Answer 3

@Romero

Answer 4

Oh yeah sorry typo but I do know what all pivot columns make up the basis for Col A but can you tell me why @myko

Answer 5

Col A means vector space formed by column vectors of your matrix. So when you have your matrix in echalon form by performing raw operations there will be so called pivot colum vectors that are the only independent column vectors in the matrix...