Question 5.E.8.1: Evaluate the following convolutions. (a) (1 2 3) ⊙ (4 5 6). ......

Matrix Analysis and Applied Linear Algebra [1113429]

Evaluate the following convolutions.

(a) $\begin{pmatrix}1\\2\\3\end{pmatrix} \odot \begin{pmatrix}4\\5\\6\end{pmatrix}.$ (b) $\begin{pmatrix}-1\\0\\1\end{pmatrix} \odot \begin{pmatrix}1\\0\\-1\end{pmatrix}$ (c) $\begin{pmatrix}1\\1\\1\end{pmatrix} \odot \begin{pmatrix}α_0\\α_1\\α_2\end{pmatrix}.$

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(a) $\begin{pmatrix}4\\13\\28\\27\\18\\0\end{pmatrix}$ (b) $\begin{pmatrix}-1\\0\\2\\0\\-1\\0\end{pmatrix}$ (c) $\begin{pmatrix}α_0\\α_0 + α_1\\α_0 + α_1 + α_2\\α_1 + α_2\\α_2\\ 0 \end{pmatrix}$

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