Consider the following system: $$x_1+ 3x_2=6$$ $$-5x_1+kx_2=…

Consider the following system: $$x_1+ 3x_2=6$$ $$-5x_1+kx_2= h$$   a) Determine $h$ and $k$ such that the system above has no solution.   b) Determine $h$ and $k$ such that the solution set of the system contains a unique solution   c) Determine $h$ and $k$ such that the solution set of the system contains many solutions.  

Find all solutions, if any exist, of the following system. I…

Find all solutions, if any exist, of the following system. If the system has multiple solutions, write the solution set as the Span of some vectors. $$\begin{matrix}&2 x_1 &-5 x_2 &+ x_3 &-6 x_4 &+ 2 x_5 &= 0\\&-8 x_1 &+20 x_2 &-4 x_3 &+24 x_4 &-8 x_5 &= 0\\&-6x_1&+15 x_2 &- x_3 & & -4 x_5 &= 0\\& & &- x_3 & +9 x_4 & &= 0\\& & &2 x_3 &- 18 x_4&+ x_5 & = 0\end{matrix}$$