第14章 14.1

(1)

$A+2B=\begin{pmatrix}1&-2\\3&0\end{pmatrix}+2\begin{pmatrix}-3&2\\4&-1\end{pmatrix}=\begin{pmatrix}-5&2\\11&-2\end{pmatrix}$

(2)

$2A-3B=2\begin{pmatrix}1&-2\\3&0\end{pmatrix}-3\begin{pmatrix}-3&2\\4&-1\end{pmatrix}=\begin{pmatrix}11&-10\\-6&3\end{pmatrix}$

(3)

$AB=\begin{pmatrix}1&-2\\3&0\end{pmatrix}\begin{pmatrix}-3&2\\4&-1\end{pmatrix}=\begin{pmatrix}-3-8&2+2\\-9&6\end{pmatrix}=\begin{pmatrix}-11&4\\-9&6\end{pmatrix}$

(4)

$BA=\begin{pmatrix}-3&2\\4&-1\end{pmatrix}\begin{pmatrix}1&-2\\3&0\end{pmatrix}=\begin{pmatrix}-3+6&6\\4-3&-8\end{pmatrix}=\begin{pmatrix}3&6\\1&-8\end{pmatrix}$

(5)

$A^2=\begin{pmatrix}1&-2\\3&0\end{pmatrix}\begin{pmatrix}1&-2\\3&0\end{pmatrix}=\begin{pmatrix}1-6&-2\\3&-6\end{pmatrix}=\begin{pmatrix}-5&-2\\3&-6\end{pmatrix}$

(6)

$(A+B)(A-B)=\begin{pmatrix}-2&0\\7&-1\end{pmatrix}\begin{pmatrix}4&-4\\-1&1\end{pmatrix}=\begin{pmatrix}-8&8\\28+1&-28-1\end{pmatrix}=\begin{pmatrix}-8&8\\29&-29\end{pmatrix}$