Let \(\left\{\mathbf{X}_{n}ight\}\) be a sequence of \(d\)-dimensional random vectors where \(\mathbf{X}_{n} \xrightarrow{d} \mathbf{Z}\) as \(n ightarrow \infty\) where \(\mathbf{Z}\) has a \(\mathbf{N}(\mathbf{0}, \mathbf{I})\) distribution. Let \(\mathbf{A}\) be a \(m \times d\) matrix and let \(\mathbf{b}\) be a \(m \times 1\) real valued vector. Fnd the asymptotic distribution of the sequence \(\left\{\mathbf{A X}_{n}+\mathbf{b}ight\}_{n=1}^{\infty}\) as \(n ightarrow \infty\). Describe any additional assumptions that may need to be made for the matrix \(\mathbf{A}\) and the vector \(\mathbf{b}\). What effect does adding the vector \(\mathbf{b}\) have on the asymptotic result?