Mar 4, 2025 · The pivots do not tell use which columns are linearly independent. Linear independence isn't a property that a column either does or does not have. It is a property of …

I have a very hard time remembering which is which between linear independence and linear dependence... that is, if I am asked to specify whether a set of vectors are linearly dependent …

A set of vectors is linearly dependent when there are an infinite amount of solutions to the system of equations. This is non-trivial? Where does no solution come in? I understand that if there is …

Can the determinant (assuming it's non-zero) be used to determine that the vectors given are linearly independent, span the subspace and are a basis of that subspace?

Feb 23, 2017 · Any set of linearly independent vectors can be said to span a space. If you have linearly dependent vectors, then there is at least one redundant vector in the mix.

None of the columns are multiples of the others, but the columns do form a linearly dependent set. You know this without any real work, since $3$ vectors in $\mathbb {R}^2$ cannot form a …

Sep 5, 2015 · To me linearly independence is one of those math definitions that it is easier to get the feeling with characterisations (in this case something that isn't linearly dependent), rather …

Jan 24, 2016 · Yes, if you can convert the matrix into reduced row echelon form (or even just row echelon form) without a row of 0 0 s,then the vectors are linearly independent.

12 you can take the vectors to form a matrix and check its determinant. If the determinant is non zero, then the vectors are linearly independent. Otherwise, they are linearly dependent.

Jul 23, 2017 · Well i'm reading in a book that the rank of a matrix is equal to the maximum number of linearly independent rows or, equivalently, the dimension of the row space.