- #1
Chen
- 977
- 1
I have a couple of questions on this subject that I need help with.
1. Let v1, v2 and v3 be three linearly dependent vectors. Prove or disprove that the following vectors are also linearly dependent:
v1+v2, v1+v3, v2+v3
2. Let S = {v1, v2, v3, v4, v5} be a set of five vectors in a vector space V over a field F. Prove or disprove that if every subset T of S so that T!=S is linearly independent, S is also linearly idependent.
1. Let v1, v2 and v3 be three linearly dependent vectors. Prove or disprove that the following vectors are also linearly dependent:
v1+v2, v1+v3, v2+v3
2. Let S = {v1, v2, v3, v4, v5} be a set of five vectors in a vector space V over a field F. Prove or disprove that if every subset T of S so that T!=S is linearly independent, S is also linearly idependent.