Question #2a1c5

1 Answer
Jan 31, 2018

The answer is YES. See below

Explanation:

Let #V# a vector space of dimension n.
For this reason there is (almost) a base with n vectors #B={vecv_1,vecv_2,...vecv_n}#
Because is a base this set is generator and linearly independent.
If we consider #B'={vecv_1,vecv_2,...vecv_(n-1)}#the first n-1 vectors of that base, those vector remains linearly independents and will be a generator sistem of a certain linear subvariety of #V#

Example

let #RR^3# and #B={vecv_1, vecv_2,vecv_3}# a base of #RR^3#. Even the canonic one #(1,0,0)=vecv_1, (0,1,0)=vecv_2 and (0,0,1)=vecv_3#. If we consider #{vecv_1,vecv_2}# those vectors generate the plane XY and are linearly independents (in the plane and in #RR^3#) because wichever linear combination of #vec0# forces to all coefficients be equal to 0 (by definition of base)