H.W_1: Consider the characteristic equation of system: s7 + 3s6 +355 + sª + s³ + 3s² + 3s + 1 = 0 Use Routh-Hurwitz criterion, determine the number of roots with positive real parts. Comment on the stability of the system.

Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.

Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.

What is a system of linear equations in the variables x, y, and z?