Not homework, test review - help with determining valid subspaces 10) Determine which of the following sets is a subspace of Pn for an
    appropriate value of n.

EXPLAIN/PROVE WHY OTHERS ARE NOT VECTOR SPACES.

All polynomials of the form p(t) = a + bt2, where a and b are in R.
B: All polynomials of degree exactly 4, with real coefficients.
C: All polynomials of degree at most 4, with positive coefficients.


A) A only B) A and B C) B only D) C only

The answer is A  (A only). WHY?


*

*I see that A is closed under scalar mult and vector addition, and
includes the zero vector.

*But isn't B also closed unser scalar mult, vec addition, and inc. zero vector?

*Am I correct that C is not a subspace because the positive coefficients make zero vector impossible?
Test is on Monday; don't really have the opportunity to go to campus and ask my professor.
