if v1= [1 v2 =[2 v3=[2 v4=[1 v5 = [3 2] 3] 4] 1] 6] u0=[1 u1=[1 u2=[2 u3=[-1 u4=

Question

if v1= [1         v2 =[2     v3=[2      v4=[1    v5 = [3           2]                3]           4]            1]             6] u0=[1     u1=[1           u2=[2            u3=[-1     u4=[4     u5=[1        0             2                  1                     4           4            1        0]           -1]                  -2]                    6]          0]           0] 1.Is the set{v1, v3} linearly independent or linearly dependent? 2.Is the set{v2, v3} linearly independent or linearly dependent? 3.Is the set{v2, v3, v4} linearly independent or linearlydependent? 4.Is the set{u3, u4} linearly independent or linearly dependent? 5.Is the set{u1, u4, u5} linearly independent or linearlydependent? 6.Is the set{u0, u1, u4} linearly independent or linearlydependent? 7.Is the set{u0, u1, u2, u4} linearly independent or linearlydependent? 8.If youanswered that the set is linearly dependent, write one of thevectors as a linear combination of the others foreach. I need answers asap, solution can be posted later need help !
if v1= [1         v2 =[2     v3=[2      v4=[1    v5 = [3           2]                3]           4]            1]             6] u0=[1     u1=[1           u2=[2            u3=[-1     u4=[4     u5=[1        0             2                  1                     4           4            1        0]           -1]                  -2]                    6]          0]           0] 1.Is the set{v1, v3} linearly independent or linearly dependent? 2.Is the set{v2, v3} linearly independent or linearly dependent? 3.Is the set{v2, v3, v4} linearly independent or linearlydependent? 4.Is the set{u3, u4} linearly independent or linearly dependent? 5.Is the set{u1, u4, u5} linearly independent or linearlydependent? 6.Is the set{u0, u1, u4} linearly independent or linearlydependent? 7.Is the set{u0, u1, u2, u4} linearly independent or linearlydependent? 8.If youanswered that the set is linearly dependent, write one of thevectors as a linear combination of the others foreach. I need answers asap, solution can be posted later need help !

Explanation / Answer

ind, ind, dep, ind, ind, ind, dep 3) v2-(1/2)v3=v4 7) 4u0 + (8/3)u1 - (4/3)u2 = u4 One way to do this is to set up and solve equations. For example, Question 1: 1x= 2, 2x= 4. If there's an x that can solve the system, the vectors are dependent. Cheers!

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