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(Solved):   Let P2 be the vector space of polynomials of degree 2 or less. Consider t ...



 

Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2:B={?1+x+x2, ?1+x2, ?1?x},C={2?x+x2, 2?2x+x2, 3?2x+x2}.

  1. Find the change of basis matrix from the basis B to the basis C.

    [id]BC= []
     
  2. Find the change of basis matrix from the basis C to the basis B.

    [id]CB= [Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2:
B
=
>
{-1+3+x,
Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered bases of P2: B = > {-1+3+x, -1+z?, -1-2}, {2 – x + x², 2 – 2x + x², 3 – 2.c + x2}. ? a. Find the change of basis matrix from the basis B to the basis C. 3 2 -1 [id] = 1 2 1 -3 -3 0 b. Find the change of basis matrix from the basis C to the basis B. [id]B


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