(a) Show that the Cauchy-Euler equation a t^{2} y^{\prime \prime}+b t y^{\prime}+c y=0 can be written as aCauchy-Euler system t \mathbf{x}^{\prime}=\mathbf{A x} with a constant coefficient matrix A, by setting x₁ = y/t and x2 = y'. (b) Show that for t > 0 any system of the form (1) with A an n×nconstant matrix has nontrivial solutions of the form x(t) = tuif and only if r is an eigenvalue of A and u is a corresponding eigenvector.