What exactly does linear dependence and linear independence …
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 …
Using the Determinant to verify Linear Independence, Span and …
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 …
How to Tell If Matrices Are Linearly Independent
Jul 20, 2013 · Another alternative for testing is to check for the determinant for each matrices (this may look tedious for a complicated matrix system), If the determinant is non zero, It is said to …
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 …
Connection between linear independence, non-/trivial and x …
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 …
Orthogonality and linear independence - Mathematics Stack …
However, every orthonormal set is linearly independent by the above theorem, as every orthonormal set is an orthogonal set consisting of nonzero vectors.
Why is it called linearly independent? - Mathematics Stack Exchange
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 …
Determinant of a matrix and linear independence (explanation …
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 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.