Span and Linear Independence
Span and Linear Independence Exercise 1 Suppose $v_1, v_2, v_3, v_4$ spans $V$. Prove that the list $$v_1 - v_2, v_2 - v_3, v_3 - v_4, v_4$$ also spans $V$. Exercise 2 Verify the assertions: A list $v$ of one vector $v \in V$ is linearly independent if and only if $v \neq 0$. A list of two vectors in $V$ is linearly independent if and only if neither vector is a scalar multiple of the other. ...