Linear Independence of the Set of Vectors
Linearly Independent
Linearly dependent

(a) Test for the linear independence of the set of vectors
(0,1,0,1,1,0), (1,1,1,0,0,1), (1,0,1,0,1,1), (1,1,1,0,0,0), (0,0,1,0,1,1)
in V6 over the field of rational numbers.

(b) Test for the linear independence of the set of vectors
(1,0,1), (1,2,0), (0,1,2), (1,1,2),
in V3 over the field of rational numbers.

Solution Summary

This solution is comprised of a detailed explanation for the linear independence of the set of vectors.
It contains step-by-step explanation to test for the linear independence of the set of vectors
(0,1,0,1,1,0), (1,1,1,0,0,1), (1,0,1,0,1,1), (1,1,1,0,0,0), (0,0,1,0,1,1) in V6 over the field of rational numbers
and for the linear independence of the set of vectors (1,0,1), (1,2,0), (0,1,2), (1,1,2) in V3 over the field of rational
numbers.

... Since all the subsets of 3 column vectors of B are linearly independent, it follows that the minimal linearly dependent set of columns of B is the set {c_1,c_2 ...

... dependent set of vectors in a vector space V, and v4 is any vector in V, then {v1, v2, v3, v4} is also linear dependent. For the Linear Independence, the ...

... How do we know that a set of vectors form an independent set? An independent set is defined as: (1.12) That is, the linear combination of the basis ...

... a linearly independent set to obtain a basis, and complete a proof regarding subspaces of finite dimensional vector space. 1) Consider the given vectors as row ...

... p(x) depend on only 2 independent parameters, which leads to the idea that the set of these ... (The vectors of the basis are linear independent, since their ...

... a basis must contain only linear independent vectors If the ... n) In our example, the set of fundamental solutions will have 2 linear independent functions that ...

... That means that the vectors that form the columns of ... will consist of the columns of A that are linearly independent. ... Exercise 10 to show that the set of points ...

... 2. Find all extreme points of the following polyhedral set. ... is produced by intersection of n linearly independent lines ... the coefficients of this n vectors in as ...

... eigenvalue, we consider only a linearly independent set of eigenvectors. ... If A is diagonalizable, the set of (representative ... should be n such vectors since they ...