Please solve complete problem. I need complete step by step solution. Book: Fundamental of differential equation

3. Consider the equation y(t) 6y\"(t) + 11y 6y(t) = 0. Let x = [y, v, "]. Let A be the matrix 0 1 0 0o 0 1 6 ~11 6 (a) Compute Ax. State its connection with x'. (b) Compute the characteristic polynomial of A. Show work for credit, (c) 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 () 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