QuestionA denotes an $m \times n$ matrix. Determine whether the statement is true or false. Justify your answer. The column space of $A, \operatorname{Col} A$, is the set of all solutions of $A x=b$.
Choose the correct answer below. A. The statement is true. The column space of $A$ is $\operatorname{Col} A=\left\{b: b=A x\right.$ for some $\mathbf{x}$ in $\left.\mathbb{R}^{n}\right\}$. B. The statement is false. The column space of $A$ is the set of all solutions of $A \mathbf{x}=\mathbf{0}$. C. The statement is false. The column space of $A$ is $\operatorname{Col} A=\left\{b: b=A x\right.$ for some $\mathbf{x}$ in $\left.\mathbb{R}^{n}\right\}$. D. The statement is true. The column space of $A$ is the set of all solutions of $A \mathbf{x}=\mathbf{0}$.