(Solved): 5. Find the Jacobian matrix of the following vector-valued multi-variable functions. (a) \( f: \ma ...

5. Find the Jacobian matrix of the following vector-valued multi-variable functions. (a) \( f: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m} \) is defined by \( f(\boldsymbol{x})=\boldsymbol{A} \boldsymbol{x}-\boldsymbol{b} \), where \( \boldsymbol{x} \in \mathbb{R}^{n}, \boldsymbol{A} \in \mathbb{R}^{m \times n}, \boldsymbol{b} \in \mathbb{R}^{\mathrm{m}} \). (b) \( f: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n} \) is defined by \( f(\boldsymbol{x})=\boldsymbol{x} \boldsymbol{x}^{T} \boldsymbol{a} \), where \( \boldsymbol{x} \in \mathbb{R}^{n}, \boldsymbol{a} \in \mathbb{R}^{n} \).