Question

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 >

Answer 1

Fagu No. Date Laven Set 94N0 lincenly independent in therefore th ere exist Such that if M+V+ gW = 0 scalarg ,Y2113 Cansider, 2(-Y-3W)+B(2u+W)+Y(-4-2V) =0 2-V-39W+2 BU +BW yu -2YV=0 (ax+ fw-yu)+(-34 W+2pu-2 YV) = (-9-2Y) B0, tam pasing ue gel 28-y-0 - 2y- -0 -34 =0 salying this, wp get :--3N, 2U4W,- -N lineanly indlepen- Consider, (-3V-3w) t 8 (-4-W)+Y(-34 +3W) = 0 ul-8-3) tV(-39)+W(-39-B+8YY-0 - 34 = 0 -3x-8+3Y=0 By Solving.we get -B=Y=0 -3Y-3W, -U-hw,-g4+3 Lincoy indepadant.