I am reading the book, Applied Linear Algebra and Matrix Analysis.
When I was doing the exercise of Section2.7 Exercise 5, I was puzzled at solving it.
Here is the problem description:
With $A = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 2 & 1 \\ 1 & 0 & 1\end{bmatrix}, B = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} and C = \begin{bmatrix} 2 & -1 \\ 1 & 0\\ 1 & 3\end{bmatrix}$, and $X =[ x_{ij}]$ a 3×2 matrix of unknowns, use tensor products to determine the coefficient matrix of the linear system $AX + XB = C$ in matrix–vector form.
I did some searches in net but I still don't know to get the coefficient matrix of linear system $AX + XB = C$ in matrix–vector form.
And the answer just give a result as following:
$\begin{bmatrix} 3 & 0 & 0 & 1 & 0 & 0 \\ 2 & 4 & 1 & 0 & 1 &0 \\ 1 & 0 & 3 & 0 & 0 & 1 \\ -1 & 0 & 0 & 1 & 0 & 0 \\ 0 & -1 & 0 & 2 & 2& 1 \\ 0 & 0 & -1 & 1 & 0 & 1 \end{bmatrix} \begin{bmatrix} x_{11} \\ x_{21} \\ x_{31} \\ x_{12} \\ x_{22} \\ x_{32} \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \\ 1 \\ -1 \\ 0 \\ 3\end{bmatrix}$
So, if not mind, could anyone teach me how to solve it and give some toturials about it.
Thanks in advance.