The first five Hermite polynomials are 1, 2t, −2 + 4t 2 , −12t + 8t 3 , and 12 − 48t 2 + 16t 4 . These polynomials arise naturally in the study of certain important differential equations in mathematical physics. Show that the first five Hermite polynomials form a basis of P4.

Select the correct answer from each drop-down menu. a system of equations and its solution are given below. system a complete the sentences to explain what steps were followed to obtain the system of equations below. system b to get system b, the equation in system a was replaced by the sum of that equation and times the equation. the solution to system b the same as the solution to system a.]