Question

Consider the homogeneous linear system \(A x=0\) where
\[
A=\left(\begin{array}{rrrr}
1 & 3 & 0 & 1 \\
1 & 3 & -2 & -2 \\
0 & 0 & 2 & 3
\end{array}\right) \text {. }
\]
Identify which of the following statements are correct?
a) \(A x=0\) has no solution.
b) \(\operatorname{dim} \operatorname{ker} A=2\)
c) \(A x=0\) has a unique solution.
d) For any vector \(b \in \mathbb{R}^{3}\) the equation \(A x=b\) has at least one solution.