If I have a matrix and make it into reduced row-echelon form, how can I determine whether the vectors that form the matrix are linearly independent or dependent?
you want to know about linear dependence of vectors of a row reduced echelon form of a matrix
if it could be reduced to echlon form then its cant be linearly dependent
if vectors are linearly dependent then it cant be made into echelon form
take an example and try urself