What exactly does linear dependence and linear independence imply ...
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 or …
Using the Determinant to verify Linear Independence, Span and Basis
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?
Reduced row echelon form and linear independence
Jan 24, 2016 · Old thread, but in fact putting the vectors in as columns and then computing reduced row echelon form gives you more insight about linear dependence than if you put them in as rows. The …
How to tell if a columns of matrix are linear dependent?
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 linearly …
Connection between linear independence, non-/trivial and x solutions ...
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 no …
Orthogonality and linear independence - Mathematics Stack Exchange
However, every orthonormal set is linearly independent by the above theorem, as every orthonormal set is an orthogonal set consisting of nonzero vectors.
Determinant of a matrix and linear independence (explanation needed)
Apr 3, 2018 · The n vectors are linearly dependent iff the zero vector is a nontrivial linear combination of the vectors (definition of linearly independent). The zero vector is a nontrivial linear combination of …
linear algebra - Determine if 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.
Why do pivot columns indicate linear independence?
Mar 4, 2025 · I understand that the two pivot columns tell us which columns in our A matrix are linearly independent. I also understand that we can put this into the test equation for linear independence.
definition - Is a linear combination linearly independent ...
The vectors are linearly independent if the only linear combination of them that's zero is the one with all $\alpha_i$ equal to 0. It doesn't make sense to ask if a linear combination of a set of vectors (which …