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  • 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 independ
  • Linear independency before and after Linear Transformation
    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 linear independence of v1,⋯vn v 1, v n This condition is necessary and sufficient
  • Connection between linear independence, non- trivial and x solutions . . .
    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 no solution, then all of the vectors do not intersect at a specific coordinate (which is the solution to the system of equations)
  • Reduced row echelon form and linear independence
    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 them in as rows The key thing is that ERO's preserve linear relations between the columns So, you can row reduce, look at the corresponding columns, and typically tell at a glance not only if they were linearly independent (if so
  • Using the Determinant to verify Linear Independence, Span and Basis
    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 assuming I hav
  • linear independent rows of a matrix - Mathematics Stack Exchange
    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 mean dimension of the rowspace, dim 1, and the number of linearly independent rows is equal?
  • How to Tell If Matrices Are Linearly Independent
    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 Independent, and if the determinant is zero, it is Linearly dependent
  • 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
  • How to tell if a columns of matrix are linear dependent?
    None of the columns are multiples of the others, but the columns do form a linearly dependent set You know this without any real work, since $3$ vectors in $\mathbb {R}^2$ cannot form a linearly independent set
  • Linear dependency of polynomials question - Mathematics Stack Exchange
    @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 amounts to showing they are linearly dependent





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