the reason she can fill 1 and 1/4 tanks is because if you multiply 5 by 12 you get 60 and then you multiply 4 by 12 and its 48 so 48/60 is what you get meaning that it takes her 48 minutes to fill one tank and 48 plus 12 is 60 and 12 is 1/4 out of 48 so you get 1 and 1/4 tanks she can fill in one hour.
We're told (and we can confirm) that , so is a linear combination of the other two vectors.
This means <em>H</em> is sufficiently spanned by ; no need for the third vector.
But this also means we can write either as a linear combination of , and as a lin. com. of . So any set of these three vectors taken two at a time will span the subspace <em>H</em>. Hence all of b, c, and d are acceptable.