計算機數學

Suppose $A$ is 3 by 4, and $Ax = 0$ has exactly 2 special solutions:

$x_1 = \begin{bmatrix}3\\4\\1\\0\end{bmatrix}, \quad x_2 = \begin{bmatrix}-2\\-1\\0\\1\end{bmatrix}$

(a) (6%) Find $A$'s row reduced echelon form $R$.

(b) (8%) Find the dimensions of all four fundamental subspaces $C(A)$, $N(A)$, $C(A^T)$, $N(A^T)$.

(c) (6%) Following (b), find bases for two of these subspaces (choose two subspaces for which sufficient information is available).