Final answer:
To find the change of basis matrix from B to C, express each vector in C as a linear combination of vectors in B and solve for the coefficients, which form the columns of the matrix.
Step-by-step explanation:
The student has asked how to find the change of basis matrix from the basis B to C. To find this matrix, we need to express each vector in the new basis C in terms of the old basis B. This involves writing a system of equations for each vector in C and solving for the coefficients that multiply the vectors in B.
For example, consider the first vector in C. We would have an equation that looks like (-2-x+x²) = a(2+x+x²) + b(-2-2x-x²) + c(-1-2x-x²), and similarly for the other vectors in C. Solving for a, b, and c gives us the first column of the change of basis matrix, and we repeat this process for the second and third vectors in C.
Unfortunately, without the explicit equations, we cannot compute the actual matrix here. Moreover, the reference information provided does not directly relate to the question, thus emphasizing the need to focus solely on the procedures for finding a change of basis matrix.