Using EES (or other) software, solve these systems of algebraic equations. (a) $$ \begin{array}{r} 3 x_{1}-x_{2}+3 x_{3}=0 \\ -x_{1}+2 x_{2}+x_{3}=3 \\ 2 x_{1}-x_{2}-x_{3}=2 \end{array} $$ (b) $$ \begin{aligned} 4 x_{1}-2 x_{2}^{2}+0.5 x_{3} &=-2 \\ x_{1}^{3}-x_{2}+x_{3} &=11.964 \\ x_{1}+x_{2}+x_{3} &=3 \end{aligned} $$

Question: Solve the following systems of algebraic equations using the provided steps: System (a): $$ 3x_1 - x_2 + 3x_3 = 0 \\ -x_1 + 2x_2 + x_3 = 3 \\ 2x_1 - x_2 - x_3 = 2 $$ System (b): $$ 4x_1 - 2x_2^2 + 0.5x_3 + 2 = 0\\ x_1^3 - x_2 + x_3 - 11.964 = 0\\ x_1 + x_2 + x_3 - 3 = 0 $$ Answer: For system (a), following the steps for solving a linear system of equations, we find the solution to be: $$ x_1 = 1\\ x_2 = 1\\ x_3 = 2 $$ For system (b), we set up the problem to be solved using an iterative method such as the Newton-Raphson method with the given Jacobian matrix and vector function. To find the solution, we must use a software tool, such as EES or another preferred tool capable of solving systems of nonlinear algebraic equations. A good initial guess must be provided, and the solution will depend on the chosen method's convergence properties.