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- Let x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if anything, can weconclude about the possible values of |xTy|?Which of the following sets of vectors are linearly independent.Are the following sets of vectors linearly independent? Show the details of your work. [3 4 0 1], [2 -1 3 5], [1 6 -8 -2]
- The vectors are linearly independent if and only if k ≠ ___S is a linearly independent set,then for any x element of , x is not the linear combination of other vectors in S. Is this true or false?If there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multipleof one of the other vectors. Is the set S linearly independent or linearly dependent?
- If {v1, v2, . . . , vn} is a linearly dependent set of vectors, prove thatone of these vectors is a linear combination of the other.Use a counterexample to show that the following statement is false: if a, b and c are nonzero vectors in R^2, then c is a linear combination of a and b.Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W contains n + 1 distinct vectors, W is linearly dependent.