I have seen similar problems on the site but when I apply those methods to my problem, my solution does not match up with the supposed correct answer shown in the image. I know that "If a set is LI and has the same dimensions as the vector space, then it is a basis of V". This set is in fact LI because when I do the method of c1v1 + c2v2 = 0, I get that c1 = c2 = 0 which means LI. Also, when I put the vectors in matrix form and find the rank, I get that the rank is two which matches the dimension of the vector space which indicates, to me, that the set spans P2.
Can someone clarify the method I should be using to approach these problems with polynomials?
Best Answer
0 is in the first set, so it cannot be linearly independent, since $x_10=0$ does not imply $x_1=0$.
The rank of the second set is in fact two, but the dimension of the space is 3. Thus it cannot span $P_2$.