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 …

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.

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.

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 $6$ …

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, …

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 …

Nov 24, 2025 · The statement of linear independence seems garbled: it should be that f, g, h f, g, h are linearly independent if and only if c1 ≠ 0,c2 ≠ 0,c3 ≠ 0 c 1 ≠ 0, c 2 ≠ 0, c 3 ≠ 0 such that the linear …

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 …

Jun 8, 2023 · Eigenvectors of different eigenvalues are linearly independent (without matrices) Ask Question Asked 2 years, 8 months ago Modified 2 years, 8 months ago

Closed 3 years ago. How can I prove that if I have n n eigenvectors from different eigenvalues, they are all linearly independent?