Finding Dimensions of Vector Subspace Spanning a Set

[Pearce_09]

The functions e^x and e^2x
I have to find the dimmensions of the vector subspace spanning the set.
I understand how to solve other problems like involving matrices and row reducing, but this function i don't know where to start and how to figure out the dimensions. Any help would be greatly appriciated
thanks
adam

 

[Perses]

You need to show if it is independent or not to find the basis and consequently the dimension. The first equation is ae^x + be^2x = 0; which you know. To find another, try differentiating the equation and then manipulating these equations to isolate for one of the two terms(ie, e^x or e^2x). Since this is a function, The equation should hold true for all values of t. perhaps try some that will give you an answer for one of the constants a or b.