The discussion revolves around the properties of vector spaces, specifically addressing whether a set of 6 vectors in R5 can form a basis for R5. The subject area is linear algebra, focusing on concepts of linear dependence, spanning sets, and the definition of a basis.
Some participants express agreement with the assertion that a set of 6 vectors cannot be a basis for R5 due to linear dependence. Others provide definitions related to the properties of a basis, indicating a productive exploration of the topic.
There is an emphasis on the definitions and properties of a basis in finite-dimensional vector spaces, as well as the implications of having more vectors than the dimension of the space.
NewtonianAlch said:Homework Statement
A set of 6 vectors in R5 cannot be a basis for R5, true or false?
The Attempt at a Solution
I'm thinking true, because any set of 6 vectors in R5 is linearly dependent, even though some sets of 6 vectors in R5 span R5.
To be a basis it must be a linearly independent spanning set, so if it's linearly dependent, it cannot be a basis.
Am I correct?