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 …

3 Suppose v1,⋯vn v 1, v n are linearly independent and T is a linear transformation. Suppose ker (T) only intersects linear span W W of v1,⋯vn v 1, v n only at {0} {0}. Then T preserves the …

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 …

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? (In other words …

Oct 4, 2017 · Well i'm reading in a book that the rank of a matrix is equal to the maximum number of linearly independent rows or, equivalently, the dimension of the row space. So does that …

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 …

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.

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 …

Feb 23, 2017 · Any set of linearly independent vectors can be said to span a space. If you have linearly dependent vectors, then there is at least one redundant vector in the mix.

Mar 17, 2013 · @HarryStuart : Three vectors in a $3$-dimensional space span the space if and only if they are linearly independent. Showing that a nonzero solution exists in this case …