Answer with Step-by-step explanation:
We are given that are in
and
is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.
We have to find that given statement is true or false.
Dependent vectors:Dependent vectors are those vectors in which atleast one vector is a linear combination of other given vectors.
Or If we have vectors
Then their linear combination
There exist at least one scalar which is not zero.
If are dependent vectors then
for scalars
Then , by definition of dependent vectors
There exist a vector which is not equal to zero
If vector is a linear combination of
, So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.
Hence, by definition of dependent vectors
{} is linearly dependent.
Option B is true.