Of course;)

It can be done, but you would have to catch the earliest train from Zürich, then to Täsch, onto Zermatt and up to Gornergrat. It would take you around 5hrs just to get up there. Then the last train leaves Gornergrat station back to Zermatt at 6PM (maybe earlier on winter, not sure). So in the end transportation time alone will be around 9-10hrs. I'd recommend spending a night in Zermatt, to avoid the hassle and exhaustion

O último trem sai de Zermatt em direção ao Gornergrat às 19h24 e o último retorno sai de Gornergrat às 20h07. Mas, já deve ser noite escura. Se fores, sentes na direita do trem que é onde tens a melhor visão. Os últimos trens são de hora em hora e mais cedo a cada 24 minutos.

Walk up the road at the end of the village, buy a ticket on the tram and enjoy the day

I'd be inclined to take the chairlift instead if you have the time and money. It's a more spectacular ride, and I've done both. Look for Glacier Paradise rather than the train. Best to book on the spot because you don't want to waste money if the weather is no good.

Take the train ticket to the top. Enjoy the views.

Hi there, the best solution would be to go by train - you can book a day return from Basel SBB to Zermatt. The journey takes @ 3hr 40 mins. If you want to get into the mountains , I would recommend the Gornergrat - The Matterhorn experience - book the ticket via SBB website - train goes from Basel SBB to Zeramatt and you then take the Gornergrat train from Zermatt into the mountains (2815 m above sea level ) to get not only a great view of the Matterhorn plus 29 other peaks!