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 …
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 …
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?
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.
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 3 vectors in R2 R 2 cannot form a linearly independent set.
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 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 be Linearly …
What does it mean when we say a variable changes linearly?
Aug 4, 2021 · I have attached a screenshot in which a variable is defined for an object somehow that it linearly decreases from 500 micrometers at the top of the object to 50 micrometers at the bottom of …
How to prove that eigenvectors from different eigenvalues are linearly ...
Closed 3 years ago. How can I prove that if I have n n eigenvectors from different eigenvalues, they are all linearly independent?
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.