If the determinant is non zero, then the vectors are linearly independent. Otherwise, they are linearly dependent. For homogeneous systems this happens precisely when the determinant is non-zero.
Determine whether the set of polynomials are linearly independent or dependent HD - Duration: 8:30. As before, consider the homogeneous system.
Reducing to echelon form gives.
A vector space can be of finite-dimension or infinite-dimension depending on the number of linearly independent basis vectors.
Introduction to linear dependence and independence. Linear dependence and independence. The term to use is always linearly independent or dependent regardless how many dimensions are involved. The vectors are linearly dependent, since the dimension of the vectors smaller than the number of vectors. While this method can be quick and easy, do not forget the logical progression from the definition of linear independence through homogeneous system of equations which makes .