B, D.
Option A)
The dimension of x and b gives the dimension of matrix A.
For this option, the Dimension of matrix A must be 3 * 4.
Since the number of rows is less than the number of columns, the matrix may have zero solutions OR infinite solutions.
Option A is just a single solution, Therefore It is false.
Option B)
From the similar reasoning above, option B is a possible solution since it is infinite solution for Ax = $\begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}$.
Option C)
For this option, the dimension of the matrix must be 3 * 2.
In the complete solution, it is given that $\begin{bmatrix} 1\\ 2\end{bmatrix}$ solves Ax = $\begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}$.
It is also given that $\begin{bmatrix} 1\\ 2\end{bmatrix}$ solves Ax = 0. It is a contradiction and therefore, option C is false.
Option D)
From the similar reasoning of option C, it is possible for option D to be true.
