Consider the following set of polynomials in P3 S x22x x22 1

Consider the following set of polynomials in P3: S= {x²-2x, x²-2, 1+x}. Is the following set S linearly independent?

Solution

Yes, these sets are linearly independent because no factors of any of the polynomial exist.

Means,

we can\'t write X2-2X, X2-2 as a linear function.

only 1+X is linearly dependent.