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 …
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.
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 …
linear algebra - Does a system with infinite solutions have linearly ...
Feb 10, 2022 · The solution in the question is totally wrong. "Therefore it is linearly dependent as X1=/=X2." That is wrong. "This is because for a function to be linearly independent, …
linear algebra - Find the largest possible number of linearly ...
Aug 28, 2025 · Once you know that $\ {v_4, v_5, v_6 \} \subseteq \operatorname {span} (v_1, v_2, v_3)$ and that the first three vectors form a linearly independent set, you know that the span of all $6$ …
Why is the determinant zero iff the column vectors are linearly …
The determinant of a square matrix is zero if and only if the column vectors are linearly dependent. I see a lot of references to this all over the web, but I can't find an actual explanation for t...
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 …
How to prove that eigenvectors from different eigenvalues are linearly ...
How to prove that eigenvectors from different eigenvalues are linearly independent [duplicate] Ask Question Asked 14 years, 11 months ago Modified 4 years, 1 month ago
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 …
Why is this true of matrices? Linearly dependent rows make linearly ...
Apr 13, 2023 · The rows of the original matrix are linearly dependent. The rows of the row reduced matrix are linearly dependent. There are rows of $0$ 's in the row reduced matrix. The columns of …