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 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 …

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 …

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 …

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 …

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 …

Jun 8, 2023 · Eigenvectors of different eigenvalues are linearly independent (without matrices) Ask Question Asked 2 years, 7 months ago Modified 2 years, 7 months ago

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, …

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 prove that eigenvectors from different eigenvalues are linearly independent [duplicate] Ask Question Asked 14 years, 10 months ago Modified 4 years, 1 month ago