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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.
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