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linear algebra help.?
k. my prof doesn't do examples on lecture, she only does proofs and theorems, and i can't find sufficient examples on the book.
anyways, the problem is:
Let V = R3 (space of polynomials with degree at most 3)
give a basis for V which includes the vector [ 1 1 2 ]
i don't need step-by-step solutions. i just want to have some hints on how to solve this thing.
1 Answer
- Anonymous1 decade agoFavorite Answer
Your question is a bit confusing.
Polynomials with degree at most 3 is a 4 dimensional space.
The vector you've written is 3 dimensional (that would be the same as polynomials with degree at most 2).
Anyways, in 3 dimensional space (this could be a space of polynomials or any other space - doesn't really matter), a basis could be:
[1 1 2], [1 0 0] , [0 1 0]
or [1 1 2], [1 0 0], [0 0 1]
for example. There are lots of posibilites. The only rule is, the vectors must be linear independent. And the number of vectors must be the same as the dimension of the space (3 in our case)