Don't know how to answer: Let β = {1 − x, 2x + x 2 , 3 + 2x 2 } is a base of p2 ...
1.Let β = {1 − x, 2x + x 2 , 3 + 2x 2 } is a base of p2 (the vector space of the polynomials of degree less than or equal to 2).
two. On P2 consider the inner product
< u, v >= a0b0 + a1b1 + a2b2
where u = a0 + a1x + a2x^2 and v = b0 + b1x + b2x^2 are two vectors from P2.
a)Verify that the base β is orthogonal to this inner product.
b)Find an orthogonal basis for P2, according to the inner product presented.
c)Find an orthonormal basis for P2, according to the inner product presented.
1.Let β = {1 − x, 2x + x 2 , 3 + 2x 2 } is a base of p2 (the vector space of the polynomials of degree less than or equal to 2).
two. On P2 consider the inner product
< u, v >= a0b0 + a1b1 + a2b2
where u = a0 + a1x + a2x^2 and v = b0 + b1x + b2x^2 are two vectors from P2.
a)Verify that the base β is orthogonal to this inner product.
b)Find an orthogonal basis for P2, according to the inner product presented.
c)Find an orthonormal basis for P2, according to the inner product presented.
