Bab 15 Matriks

Contoh:
$\begin{array}{l}(a)(ab)\left(\begin{array}{l}c\\ d\end{array}\right)=(ac\text{ + }bd)\\ 1\times 2\text{ 2}\times 11\times 1\\ \\ (b)\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{l}e\\ f\end{array}\right)=\left(\begin{array}{l}ae+bf\\ ce+df\end{array}\right)\\ \text{ 2}\times 2\text{ 2}\times 1\text{ 2}\times 1\end{array}$

$\begin{array}{l}(c)\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{cc}e& f\\ g& h\end{array}\right)=\left(\begin{array}{cc}ae+bg& af+bh\\ ce+dg& cf+dh\end{array}\right)\\ \text{ 2}\times 2\text{ 2}\times 2\text{ 2}\times 2\\ \\ (d)\left(\begin{array}{l}a\\ b\end{array}\right)(cd)=\left(\begin{array}{cc}ac& ad\\ bc& bd\end{array}\right)\\ \text{ 2}\times 1\text{ 1}\times 2\text{ 2}\times 2\end{array}$

$\begin{array}{l}(e)\left(abc\right)\left(\begin{array}{l}d\\ e\\ f\end{array}\right)=(ad\text{ + }be+cf)\\ \text{ 1}\times 3\text{ 3}\times 1\text{ 1}\times 1\\ \\ (f)\left(\begin{array}{cc}a& b\\ \begin{array}{l}c\\ e\end{array}& \begin{array}{l}d\\ f\end{array}\end{array}\right)\left(\begin{array}{l}g\\ h\end{array}\right)=\left(\begin{array}{l}ag+bh\\ cg+dh\\ eg+fh\end{array}\right)\\ \text{ 3}\times 2\text{ 2}\times 1\text{ 3}\times 1\end{array}$

$\begin{array}{l}(a)\left(\begin{array}{cc}3& -5\\ 1& 2\end{array}\right)(3\text{ 7})\\ \text{ 2}\times \boxed{2}\boxed{1}\times 2\leftarrow \boxed{2}\ne \boxed{1}\therefore \text{ Tidak boleh didarab}\text{.}\end{array}$

$\begin{array}{l}b)\left(\begin{array}{cc}2& 9\\ 1& 3\end{array}\right)\left(\begin{array}{l}8\\ 6\end{array}\right)\\ \text{ 2}\times \boxed{2}\boxed{2}\times 1\leftarrow \boxed{2}=\boxed{2}\therefore \text{ Boleh didarab}\text{.}\\ \text{ Peringkat matriks yang terhasil}=2\times 1\end{array}$

$\begin{array}{l}(c)(-10-\text{6})\left(\begin{array}{l}7\\ 2\end{array}\right)\\ \text{ 1}\times \boxed{2}\boxed{2}\times 1\leftarrow \boxed{2}=\boxed{2}\therefore \text{ Boleh didarab}\text{.}\\ \text{ Peringkat matriks yang terhasil }=1\times 1\end{array}$

$\begin{array}{l}(d)\left(\begin{array}{l}8\\ 6\end{array}\right)\left(\begin{array}{cc}2& 9\\ 1& 3\end{array}\right)\\ \text{ 2}\times \boxed{1}\boxed{2}\times 2\leftarrow \boxed{1}\ne \boxed{2}\therefore \text{ Tidak boleh didarab}\text{.}\end{array}$

$\begin{array}{l}(e)\left(\begin{array}{l}7\\ -3\end{array}\right)(2\text{ 10})\\ \text{ 2}\times \boxed{1}\boxed{1}\times 2\leftarrow \boxed{1}=\boxed{1}\therefore \text{ Boleh didarab}\text{.}\\ \text{ Peringkat matriks yang terhasil }=2\times 2\end{array}$