1.9 Vector subspaces

Which of these are subspaces?

•     [No]
•     [Yes]
• $V={\mathbb{R}}^5$ , $W=\{x:x_4=0,x_5=0\}$ [Yes]
• $V={\mathbb{R}}^5$ , $W=\{x:x_4=1,x_5=1\}$ [No]
• $V=C[0,1]$ , $W=$ {polynomials of degree $N$ } [Yes]
• $V=C[0,1]$ , $W=\{f:f$ is bandlimited to $B$ } [Yes]
• $V={\mathbb{R}}^N$ , $W=\{x:x\mathrm{hasnomorethan}5\mathrm{nonzerocomponents},\mathrm{i}.\mathrm{e}.,{∥x∥}_0\le 5\}$ [No]