need help with question 2

Question 1 [4 Marks] Let po(r). . . . . p.(r) be n + 1 polynomials of degree 0, 1,.. ., n, re- spurtheb, over a field F. Prove that {po(). ... . pa(r)} is a basis of P. (F), the vector space of all polynomials of degree n or less over F. Question 2 [5 Marks] Let A be an n Xn symmetric matrix over R, having distinct eigenvalues lisde..s, de, where &' S n. Prove that R" = EMO E.. O . . . Ex. where Ey, denotes the eigenspace of A corresponding to A,, 1