I have to determine the dimension and base of this vector space:
$\langle 2,t,\sin^2(t),\cos^2(t)\rangle $
I did this:
$\langle 2,t,\sin^2(t),\cos^2(t)\rangle =\langle 2,t,\sin^2(t)+\cos^2(t),\cos^2(t)\rangle =\langle 2,t,1,\cos^2(t)\rangle =\langle 1,t,\cos^2(t)\rangle $
So this is the base and the dimension is $3$. Am I right? How can I prove those 3 are independent of each other?
Regards, Kevin