Null Space of a Matrix

>>9171128
You're correct. Now you just have to find the vectors [math]v[/math] for which [math]Iv=0[/math]

>>9171133
So is the nullspace just
0
0
0
?

>>9171128

This is the Vandermonde matrix, which transforms the coefficients of a quadratic polynomial into its values at a, b, and c.

The nullspace is given by expanding (x-a)(x-b)(x-c) and looking a the coefficients.

>>9171137
Yep. Now if you know rank-nullity, you can deduce what the column space is.

>>9171128

The determinant is nonzero so it has full rank.

Sorry it took me a while, new to linear algebra, so is the Row Space the rows of the RREF of Matrix A so {100} {010} and {001}
And is the Column space all columns of the original matrix which have a pivot column so:
1 a a^2
{1} {b} {b^2}
1 c c^2