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 ![x_1,x_2,....x_n](https://tex.z-dn.net/?f=x_1%2Cx_2%2C....x_n)
Then their linear combination
![a_1x_1+a_2x_2+.....+a_nx_n=0](https://tex.z-dn.net/?f=a_1x_1%2Ba_2x_2%2B.....%2Ba_nx_n%3D0)
There exist at least one scalar which is not zero.
If
are dependent vectors then
for scalars ![a_1,a_2,a_3](https://tex.z-dn.net/?f=a_1%2Ca_2%2Ca_3)
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.