let u1 u2 uk be a linearly independent set of vectors in rn and let v be a vector in rn such tha

Name: let u1 u2 uk be a linearly independent set of vectors in rn and let v be a vector in rn such that v c1u1 c2u2 ckuk for some scalars c1 c2 ck with c1 not equal to 0 prove that v u2 uk note no 35103
Uploaded: 2023-03-05T13:28:07-08:00
Duration: 3 min 9 s
Channel: Sri K
Description: let u1 u2 uk be a linearly independent set of vectors in rn and let v be a vector in rn such that v c1u1 c2u2 ckuk for some scalars c1 c2 ck with c1 not equal to 0 prove that v u2 uk note no 35103

Question

Anna D. · Accepted Answer

1. We are given that the set {u1, u2, ..., uk} is linearly independent.

Question

Let { u1, u2, ..., uk } be a linearly independent set of vectors in Rn, and let v be a vector in Rn such that v = c1u1 + c2u2 + ... + ckuk for some scalars c1, c2, ..., ck with c1 not equal to 0. Prove that { v, u2, ..., uk } (NOTE: NO u1) is linearly independent.

Please give Ace some feedback