Given the following set of the vectors from M22 11 0 0 1 0 0 1 S = 0 0 1 1 0 1 11 Sis the spanning set. Select one: O True O False
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- is the ffollowing set of vectors in P2 is liner independen? Prove the answerConsider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S = {u1, u2, u3} is a spanning set for R3.Let v1, . . . , vp be vectors in R n . Show that if vp ∈ span{v1, . . . , vp−1}, then span{v1, . . . , vp−1} = span{v1, . . . , vp}.
- Let {x1, x2,...,xk} be a spanning set for a vector space V. (a) If we add another vector, xk+1, to the set, will we still have a spanning set? Explain. (b) If we delete one of the vectors, say, xk, from the set, will we still have a spanning set? Explain.Show that the set as;S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a linearcombination of vectors is S.Let the set S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R3, write the vector (4,6, 7) as a linear combination of vectors S.
- 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?Suppose {u1,u2,...,un} is a set of vectors that span V, and that {v1,v2,...,vk} is an independent set of vectors in V. Explain whyv1=x1u1+x2u2+...+xnunmust have a nontrivial solution. Explain why we may assume x1≠0. (Hint: x1 is the first unknown because u1 was the first vector in our spanning set.) Explain why this means u1 is in the span of {v1,u2,...,un} Explain why this means {v1,u2,...,un} also spans V.The set of vector {e1 ,e2 , e3 } are spaning set of R3 Select one: True False
- Determine whether the following collection of vectors in R4 is independent or dependent. Show your work.write the following vectors as linear combinations of e1, e2 and e3Determine if S is a spanning set for Rn & if Sis linearly independent. Determine if the given vector ~v is in the span of S if YES, determine if the given vector ~ can be written as a linear combination of the S vectors.