Solving problems on spanning sets© BrainMass Inc. brainmass.com February 24, 2021, 2:06 pm ad1c9bdddf
#12 a) We will not have a spanning set of V because one of two things can happen: i) x(k+1) is linearly dependent of the spanning set or ii) x(k+1) is linearly independent.
If it is i) then by definition, x(k+1) is not a member of the spanning set of V (all members must be linearly independent of each other).
On the other ...
These solves several problems regarding the addition and deletion of vectors from spanning sets.