Question

prove vectors v1= -4 +x +3x^2, v2 = 6 +5x +2x^2 v3= 8 +4x +x^2 are basis for p2(R)

Answer 1

use the coefficients of the polynomials to make vectors in R^3. Then prove that the three vectors form a basis in R^3.

Answer 2

So basically show that (-4, 1, 3), (6, 5, 2), and (8, 4, 1) form a basis in R^3.

Answer 3

Joemath,
How show form a basis, thanks much
Ameran

Answer 4

For the vectors, you can make the vectors columns in a 3 x 3 matrix, and row reduce. If you get the identity matrix, the 3 vectors form a basis.

Answer 5

Joemath314159
thank you. certainly a fan of yours..