Linear Algebra

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Basis for $P_3$

LINALG-EGBGWI

$P_3$ is the vector space of polynomials in $x$ of degree three or less with real coefficients. Which of the following are bases for $P_3$?

A

$\{1, x, x^2, x^3\}$

B

$\{x, x^2, x^3\}$

C

$\{1, 1+x, 1+x^2, 1+x^3\}$

D

$\{x^3,1-x, 1+x^2, x+x^2\}$

E

All of the above are bases for $P_3$.

F

Choices 'A' and 'C' are both bases for $P_3$.