# Bab 15 Matriks

4.9 SPM Practis (Soalan Pendek)

Soalan 1:
$\left(\begin{array}{cc}1& 4\\ 6& 2\end{array}\right)+3\left(\begin{array}{cc}2& 0\\ 4& -3\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)=$

Penyelesaian:
$\begin{array}{l}\left(\begin{array}{cc}1& 4\\ 6& 2\end{array}\right)+3\left(\begin{array}{cc}2& 0\\ 4& -3\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)\\ =\left(\begin{array}{cc}1& 4\\ 6& 2\end{array}\right)+\left(\begin{array}{cc}6& 0\\ 12& -9\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)\\ =\left(\begin{array}{cc}7& 4\\ 18& -7\end{array}\right)-\left(\begin{array}{cc}-3& 0\\ -2& -5\end{array}\right)\\ =\left(\begin{array}{cc}7-\left(-3\right)& 4-0\\ 18-\left(-2\right)& -7-\left(-5\right)\end{array}\right)\\ =\left(\begin{array}{cc}10& 4\\ 20& -2\end{array}\right)\end{array}$

Soalan 2:
Cari nilai mdalam persamaan matriks berikut:
$\left(\begin{array}{cc}9& -4\\ 5& 0\end{array}\right)+\frac{1}{2}\left(\begin{array}{cc}8& m\\ 6& -10\end{array}\right)=\left(\begin{array}{cc}13& -7\\ -2& 1\end{array}\right)$

Penyelesaian:
$\begin{array}{l}\left(\begin{array}{cc}9& -4\\ 5& 0\end{array}\right)+\frac{1}{2}\left(\begin{array}{cc}8& m\\ 6& -10\end{array}\right)=\left(\begin{array}{cc}13& -7\\ -2& 1\end{array}\right)\\ -4+\frac{1}{2}m=-7\\ \frac{1}{2}m=-3\\ m=-6\end{array}$

Soalan 3:

Penyelesaian:
2x + 8 = –2
2x = –10
x= –5

3y – 12 = 6
3y = 18
y= 6

Soalan 4:
Diberi bahawa persamaan matriks 3(6   m) + n(3   4) = (12   7),
Cari nilai m+ n.

Penyelesaian:
3(6   m) + n(3   4) = (12   7)
18 + 3n = 12
3n = –6
n= –2

3m + 4n = 7
3m + 4(–2) = 7
3m = 15
m= 5

Maka m + n = 5 + (–2) = 3