(Solved): (4) Interpret the following matrix as the coefficient matrix of a homogeneous system of linear equ ...

(4) Interpret the following matrix as the coefficient matrix of a homogeneous system of linear equations: \[ \left[\begin{array}{rrrrr} 1 & 0 & 11 & -28 & 16 \\ 0 & 1 & -1 & \frac{1}{2} & 9 \end{array}\right] \] Then find a parametrization for the solution set of this system. (5) Find a parametrization for the solution set of the following system of equations: \[ \begin{aligned} x_{1}+3 x_{2}-8 x_{3} & =6 \\ 2 x_{3} & =-4 \\ 3 x_{1}+9 x_{2}-24 x_{3}-4 x_{4} & =2 \\ -5 x_{1}-15 x_{2}+40 x_{3}+7 x_{4} & =-2 \end{aligned} \]