8. Please answer TRUE or FALSE for the following statements (NO need to justify your answer). No credit for unanswered questions; incorrect answers will deduct the credit until zero point is earned in this section.

(c) (correct: 1; incorrect: -1; unanswered: 0) $\{(0,0,0)\}$ is the orthogonal complement of $\mathbb{R}^3$ in $\mathbb{R}^3$.

(e) (correct: 1; incorrect: -1; unanswered: 0) Let $\mathbf{v}$ be a vector in $S$ and $\mathbf{u}$ be a vector such that $\langle \mathbf{u}, \mathbf{v} \rangle = 0$, then $\mathbf{u} \in S^\perp$.

(f) (correct: 1; incorrect: -1; unanswered: 0) Let $A$ be a symmetric matrix. $C(A^T)$ and $N(A^T)$ are orthogonal complement.

(h) (correct: 1; incorrect: -1; unanswered: 0) Let $U$ be a subspace of a vector space $V$. Then $(U^\perp)^\perp = U$.