Suppose we know that $S = \{v_1, v_2, v_3\}$ is a linearly independent set of
vectors in some vector space $V$ . Let $T = \{v_1 + v_2, v_2 + v_3, v_3 + v_1\}$.
Prove that $T$ is also linearly independent.
This proof makes sense to me that it would be true, but I cannot figure out the steps of the proof that make this a true statement?
Best Answer
$\det \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix} = 2 \neq 0$.