Question

T F Any set of vectors containing the zero vector is linearly dependent

Answer 1

Answer:

True

Step-by-step explanation:

Let B={$v_1, v_2,\cdots,v_k,0$} a set of vectors containing the zero vector.

B is linear dependent if exist scalars $a_0,a_1, a_2,\cdots,a_k$ not all zero such that $a_0*0+a_1*v_1+\cdots+a_k*v_k=0$.

Observe that if $a_1=a_2=\cdots=a_k=0$ and $a_0=\lambda\neq 0$ then

$\lambda*0+0*v_1+\cdots+0*v_k=0$.

Then B is linear dependent.