**4.2 Matriks Sama (Contoh Soalan)**

**Contoh 1:**

$\left(\begin{array}{cc}1& x+2\\ 4-y& -1\end{array}\right)=\left(\begin{array}{cc}1& 3\\ 2& -1\end{array}\right)$

*Penyelesaian:*$\begin{array}{l}\left(\begin{array}{cc}1& x+2\\ 4-y& -1\end{array}\right)=\left(\begin{array}{cc}1& 3\\ 2& -1\end{array}\right)\\ x+2=3\\ x=1\\ 4-y=2\\ -y=-2\\ y=2\end{array}$

**Contoh 2:**

Hitung nilai p dan nilai q dalam setiap persamaan matriks yang berikut:

$\begin{array}{l}\text{(a)}\left(\begin{array}{cc}3& 2p+q\\ p& -3\end{array}\right)=\left(\begin{array}{cc}3& 1\\ 8-2q& -3\end{array}\right)\\ \text{(b)}\left(\begin{array}{cc}10& 0\\ 5p-8& 1\end{array}\right)=\left(\begin{array}{cc}p-2q& 0\\ -4q& 1\end{array}\right)\end{array}$

*Penyelesaian:*$\text{(a)}\left(\begin{array}{cc}3& 2p+q\\ p& -3\end{array}\right)=\left(\begin{array}{cc}3& 1\\ 8-2q& -3\end{array}\right)$

2

2

*p*+*q*= 1*q*= 1 – 2

*p*----(1)

*p*= 8 – 2

*q*----(2)

Gantikan (1) ke dalam (2),

*p*= 8 – 2 (1 – 2

*p*)

*p*= 8 – 2 + 4

*p*

*p*– 4

*p*= 6

–3

*p*= 6*p*= –2

Gantikan

*p*= –2 ke dalam (1),*q*= 1 – 2(–2)

*q*= 5

$\text{(b)}\left(\begin{array}{cc}10& 0\\ 5p-8& 1\end{array}\right)=\left(\begin{array}{cc}p-2q& 0\\ -4q& 1\end{array}\right)$

10 =

*p*– 2

*q*

*p*= 10 + 2

*q*----(1)

5

*p*– 8 = –4*q*----(2)Gantikan (1) ke dalam (2),

5 (10 + 2

*q*) – 8 = –4*q*50 + 10

*q*– 8 = –4*q*14

*q*= –42*q*= –3

Gantikan

*q*= –3 ke dalam (1),*p*= 10 + 2(–3)

*p*= 4