Final answer:
The question relates to calculating coefficients for a Vandermonde interpolation polynomial, but the required matrix or relevant context is not provided. We need more information or the full question details to calculate the coefficients accurately.
Step-by-step explanation:
The student is asking for a solution to a Vandermonde interpolation problem, specifically the coefficients for a second degree polynomial P2(x) = a0 + a1x + a2x2 given a set of three points: (1.0, 6.4), (2.0, -10.2), and (3.0, -43.8). Vandermonde interpolation involves finding a polynomial that uniquely passes through all given points.
To solve this, we first need to set up the Vandermonde matrix with the given x-values and solve the system of equations for a0, a1, and a2 based on the corresponding y-values. However, without enough context or the proper Vandermonde matrix set up provided, it is not possible to solve for the coefficients accurately.
Since the provided information is either insufficient or unrelated to the Vandermonde interpolation task, and no proper matrix is supplied with the question, it is recommended to seek additional information or provide the complete task details to carry on with an accurate calculation.