1. Suppose u, V, and w is a linearly independent set (these would have to be...
(1 point) Suppose S = {r, u, d} is a set of linearly independent vectors. If x = 4r + 2u + 5d, determine whether T = {r, u, 2} is a linearly independent set. Select an Answer 1. Is T linearly independent or dependent? IfT is dependent, enter a non-trivial linear relation below. Otherwise, enter O's for the coefficients. u+ !!! I=0
Please help at an orthogonal set of three nonzero vectors u, v, w is linearly independent.
linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
1· Let S {u,v) be a linearly, independent set. Prove that(u+ v.u-v) is linearly independent. 2. Let H :2y1. Prove that H is not a subspace of f2.
Only one option is correct. Being u,v and w linearly dependent vectors of a linear space E. Then : a) u and v are linearly independent . b) u and v are linearly dependent . c) u, u + v and u + w are linearly independent . d) u, u + v and u + w are linearly dependent .
Let u = and v= Determine whether the vectors u and v are linearly independent or linearly dependent, and choose the most correct answer below. A. The vectors are linearly independent. B. We cannot easily tell whether the vectors are linearly independent or linearly dependent. C. The vectors are linearly dependent.
Given the following vectors u and v, find a vector w in R4 so that {u, v, w} is linearly independent and a non- zero vector z in R4 so that {u, v, z} is linearly dependent: 1-3 8 -8 -2 u = V= 5 -4 10 0 w=0 1- z=0 0
please help with this linear algebra question Question 10 [10 points] Let V be a vector space and suppose that {u, v, w is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {-v-3w, 2u+w, -u-2v} is linearly independent b) {-3v-3w, -u-w, -3u+3v} < Select an answer >