# Bab 15 Matriks

Soalan 3:
Diberi bahawa $Q\left(\begin{array}{cc}3& 2\\ 6& 5\end{array}\right)=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$, dengan keadaan Q ialah matriks 2 × 2.
(a)  Cari matriks Q.
(b)  Tulis persamaan linear serentak berikut dalam persamaan matriks:
3u + 2v = 5
6u + 5v = 2
Seterusnya, menggunakan kaedah matriks, hitung nilai u dan nilai v.

Penyelesaian:
$\begin{array}{l}\text{(a)}\\ Q={\left(\begin{array}{cc}3& 2\\ 6& 5\end{array}\right)}^{-1}\\ Q=\frac{1}{3\left(5\right)-2\left(6\right)}\left(\begin{array}{cc}5& -2\\ -6& 3\end{array}\right)\\ Q=\frac{1}{3}\left(\begin{array}{cc}5& -2\\ -6& 3\end{array}\right)\\ Q=\left(\begin{array}{cc}\frac{5}{3}& -\frac{2}{3}\\ -2& 1\end{array}\right)\end{array}$

Soalan 4:
Diberi bahawa $Q\left(\begin{array}{cc}3& -2\\ 5& -4\end{array}\right)=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$, dengan keadaan Q ialah matriks 2 × 2.
(a)  Cari matriks Q.
(b)  Tulis persamaan linear serentak berikut dalam persamaan matriks:
3x – 2y = 7
5x – 4y = 9
Seterusnya, menggunakan kaedah matriks, hitung nilai x dan nilai y.

Penyelesaian:
$\begin{array}{l}\text{(a)}\\ Q=\frac{1}{3\left(-4\right)-\left(5\right)\left(-2\right)}\left(\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right)\\ =-\frac{1}{2}\left(\begin{array}{cc}-4& 2\\ -5& 3\end{array}\right)\\ =\left(\begin{array}{cc}2& -1\\ \frac{5}{2}& -\frac{3}{2}\end{array}\right)\end{array}$