Q1: Let $V$ be a vector space with inner product $\langle \cdot, \cdot \rangle$. Which statement is not correct?

A1: If $x \perp y$, then $-x$ is not orthogonal to $y$.

A2: The zero vector orthogonal to the zero vector.

A3: The zero vector is orthogonal to each vector $x \in V$.

A4: If $x,y \in V$ are orthogonal, then $\langle x, y \rangle = 0$.

Q2: Let $V = \mathbb{C}^2$ be given with the standard inner product $\langle y, x \rangle = \overline{y_1} x_1 + \overline{y_2} x_2$. Which statement is correct?

A1: The vector $\binom{i}{1}$ is orthogonal to $\binom{i}{1}$.

A2: The vector $\binom{i}{1}$ is orthogonal to $\binom{-i}{1}$.

A3: The vector $\binom{1}{1}$ is orthogonal to $\binom{i}{i}$.

A4: The vector $\binom{0}{1}$ is not orthogonal to $\binom{1}{0}$.

Q3: Let $V = \mathcal{P}([0,1])$ be given with the standard inner product $\langle y, x \rangle = \overline{y_1} x_1 + \overline{y_2} x_2$. Which statement is correct?

A1: The vector $\binom{i}{1}$ is orthogonal to $\binom{i}{1}$.

A2: The vector $\binom{i}{1}$ is orthogonal to $\binom{-i}{1}$.

A3: The vector $\binom{1}{1}$ is orthogonal to $\binom{i}{i}$.

A4: The vector $\binom{0}{1}$ is not orthogonal to $\binom{1}{0}$.