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The linear independence of a set of vectors can be determined by calculating the determinant of a matrix with columns composed of the vectors in the set. If the determinant is equal to zero, then the set of vectors is linearly dependent. If the determinant is non-zero, then the set of vectors is linearly independent.What are linearly dependent vectors?
. In the theory of vector spaces, a set of vectors is said to be linearly dependent if at least one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension.What is the determinant of a vector?
This depends on the determinant of , which is Since the determinant is non-zero, the vectors and are linearly independent. Otherwise, suppose we have vectors of coordinates, with Then A is an n × m matrix and Λ is a column vector with entries, and we are again interested in A Λ = 0.Is this set linearly independent?
So this set is linearly independent. And if you were to graph these in three dimensions, you would see that none of these-- these three do not lie on the same plane. Obviously, any two of them lie on the same plane, but if you were to actually graph it, you get 2, 0. Let me say that that's x-axis. That's 2, 0, 0. Then you have this, 0, 1, 0.