Re: Span and polynomials.

my first instinct is to say check your arithmetic for your row-reduction

EDIT: also, note that you are choosing a,b,c,d arbitrarily, you are not solving for them.

Re: Span and polynomials.

Re: Span and polynomials.

Quote:

Originally Posted by

**Deveno** EDIT: also, note that you are choosing a,b,c,d arbitrarily, you are not solving for them.

Yes, that is why if I were to set each one of a, b, c, and d to 0, the system should be consistent. No?

Re: Span and polynomials.

the product on the last row in the last column should be a sum.

if your four polynomials span P3, then one linear combination (at least) must be t^3 (which is a = 1, b = c = d = 0).

this leads to 0 = -2 (from the 4th row, where your augmented column should read (d-a-2b)+(1/2)(c-2a+b)), which is inconsistent.

the zero-vector (the polynomial 0t^3 + 0t^2 + 0t + 0 in this case) is ALWAYS in the span of ANY subset.

thus setting a = b = c = d = 0 is a spectacularly bad choice for a test polynomial, because it tells us nothing (you can

always make a linear combination of 0's be 0).