Question

Can I get help with questions 2,3,4,6?

be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3 =0 (4) Consider the vectors ) 1 V3 = VA= ariables @-6-0 in R3. Compute scalars r,r2, I3, T4 not all 0 such that v, = 0. 1 Vi r2V2 +r3V3+ I4V4 = 0 tions of in W (5) Find two distinct representations of the vector as a linear combina- 3 f the vectors tion pendent (6) Prove that the set of vectors {vi,v2} is linearly independent if and only if the set of vectors {vi + v2, V1- v2} is linearly independent (7) Prove that the vectors v, V2, ..., V in R" are linearly dependent if v = 0

Answer 1

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