I need complete step by step solution asap. Book: Fundamental of differential equation

3. Consider the equation y(t) 6y"(t) + 11y' 6yit) = 0. Let x = [g.v', "]. Let A be the matrix 9 1 9 0 o0 1 6 -11 6 (a) Compute Ax. State its connection with x'. (b) Compute the characteristic polynomial of A. Show work for credit. (} Is the number 5 a root of the characteristic polynomial? Show verifica- tion. (d) Is there any connection between the coefficients of the polynomial in (c) and some numbers that have appeared in this problem? Be specific. (e) Is the matrix A diagonalizable? Quote a theorem from the book (include the page) to justify vour