- #1
negation
- 818
- 0
Homework Statement
Given that { u1, u2, u3, u4, u5, u6 } are linearly independent vectors in R16, and that w is a vector in R16 such that w ∉ span{ u1, u2, u3, u4, u5, u6 }.
a) Is the set { 0, u1, u5 } is linearly independent?
b) the set { u1, u2, u3, u4, u5, u6, w } is linearly independent?
c) the set { u1, u4, u6 } is linearly independent ?
The Attempt at a Solution
[itex]Span{u1, u2, u3, u4, u5, u6 }\in R16[/itex]
γ{ u1, u2, u3, u4, u5, u6 } = 0
(γ1u1 + γ2u2 + γ3u3 + γ4u4 + γ5u5 + γ6u6) = 0
w ∉ span{ u1, u2, u3, u4, u5, u6 } so that means there are no linear combinations for which
{ u1, u2, u3, u4, u5, u6 } spans w. How do I incorporate this into the approach?
If there are no linear combinations, then it stands to reason that the solutions to
{ u1, u2, u3, u4, u5, u6 } is inconsistent.