(Solved): State with justification, whether the fol statements are True or False : a) If a linear subspace Y ...

State with justification, whether the fol statements are True or False : a) If a linear subspace $Y$ of a normed space $X$ has a non-empty interior, then $Y=X$. b) The linear operator $\mathrm{A}:{\mathbf{C}}^2\to {\mathbf{C}}^2$, given by $A\left(z_1,z_2\right)=\left(z_1,-z_2\right)$ is a normal operator. c) Every bounded linear functional on a normed linear space is compact. d) The projection map $p:{\mathbb{R}}^3$ to ${\mathbb{R}}^3$ given by $p\left(x_1,x_2,x_3\right)=\left(x_1,x_2,0\right)$ is an open map. e) If $T:X\to Y$ is a continuous linear map, when $X$ and $Y$ are normed linear spaces, then $T$ is uniformly continuous.