Soalan 4:
$$ \text { Diberi matriks } P=\left[\begin{array}{c} \frac{1}{2} \\ -0.7 \end{array}\right] \text {, matriks } Q=\left[\begin{array}{c} 4 \\ -5 \end{array}\right] \text { dan matriks } O=\left[\begin{array}{l} 0 \\ 0 \end{array}\right] \text {, hitung } P-1.4 Q+O \text {. } $$
Penyelesaian:
$$ \begin{aligned} P-1.4 Q+O & =\left[\begin{array}{c} \frac{1}{2} \\ -0.7 \end{array}\right]-1.4\left[\begin{array}{c} 4 \\ -5 \end{array}\right]+\left[\begin{array}{l} 0 \\ 0 \end{array}\right] \\ & =\left[\begin{array}{c} \frac{1}{2} \\ -0.7 \end{array}\right]-\left[\begin{array}{c} 5.6 \\ -7 \end{array}\right] \\ & =\left[\begin{array}{c} \frac{1}{2}-5.6 \\ -0.7-(-7) \end{array}\right] \\ & =\left[\begin{array}{c} -5.1 \\ 6.3 \end{array}\right] \end{aligned} $$
$$ \text { Diberi matriks } P=\left[\begin{array}{c} \frac{1}{2} \\ -0.7 \end{array}\right] \text {, matriks } Q=\left[\begin{array}{c} 4 \\ -5 \end{array}\right] \text { dan matriks } O=\left[\begin{array}{l} 0 \\ 0 \end{array}\right] \text {, hitung } P-1.4 Q+O \text {. } $$
Penyelesaian:
$$ \begin{aligned} P-1.4 Q+O & =\left[\begin{array}{c} \frac{1}{2} \\ -0.7 \end{array}\right]-1.4\left[\begin{array}{c} 4 \\ -5 \end{array}\right]+\left[\begin{array}{l} 0 \\ 0 \end{array}\right] \\ & =\left[\begin{array}{c} \frac{1}{2} \\ -0.7 \end{array}\right]-\left[\begin{array}{c} 5.6 \\ -7 \end{array}\right] \\ & =\left[\begin{array}{c} \frac{1}{2}-5.6 \\ -0.7-(-7) \end{array}\right] \\ & =\left[\begin{array}{c} -5.1 \\ 6.3 \end{array}\right] \end{aligned} $$
Soalan 5:
$$ \text { Diberi } 4\left[\begin{array}{cc} 2 & 3 \\ -5 & b \end{array}\right]-\left[\begin{array}{cc} -4 & 9 \\ c & 0.1 \end{array}\right]=\frac{3}{5}\left[\begin{array}{cc} a & 5 \\ -35 & 1.5 \end{array}\right] \text {, hitung nilai } a \text {, nilai } b \text { dan nilai } c \text {. } $$
Penyelesaian:
$$ \begin{aligned} 4\left[\begin{array}{cc} 2 & 3 \\ -5 & b \end{array}\right]-\left[\begin{array}{cc} -4 & 9 \\ c & 0.1 \end{array}\right] & =\frac{3}{5}\left[\begin{array}{cc} a & 5 \\ -35 & 1.5 \end{array}\right] \\ {\left[\begin{array}{cc} 8 & 12 \\ -20 & 4 b \end{array}\right]-\left[\begin{array}{cc} -4 & 9 \\ c & 0.1 \end{array}\right] } & =\left[\begin{array}{cc} \frac{3}{5} a & 3 \\ -21 & 0.9 \end{array}\right] \\ {\left[\begin{array}{cc} 12 & 3 \\ -20-c & 4 b-0.1 \end{array}\right] } & =\left[\begin{array}{cc} \frac{3}{5} a & 3 \\ -21 & 0.9 \end{array}\right] \end{aligned} $$
$$ \begin{aligned} &\text { Secara perbandingan, }\\ &\begin{aligned} \frac{3}{5} a & =12 \\ a & =12 \times \frac{5}{3} \\ a & =20 \end{aligned} \end{aligned} $$
$$ \begin{aligned} 4 b-0.1 & =0.9 \\ 4 b & =1 \\ b & =\frac{1}{4} \end{aligned} $$
$$ \begin{aligned} -20-c & =-21 \\ -c & =-1 \\ c & =1 \end{aligned} $$
$$ \text { Diberi } 4\left[\begin{array}{cc} 2 & 3 \\ -5 & b \end{array}\right]-\left[\begin{array}{cc} -4 & 9 \\ c & 0.1 \end{array}\right]=\frac{3}{5}\left[\begin{array}{cc} a & 5 \\ -35 & 1.5 \end{array}\right] \text {, hitung nilai } a \text {, nilai } b \text { dan nilai } c \text {. } $$
Penyelesaian:
$$ \begin{aligned} 4\left[\begin{array}{cc} 2 & 3 \\ -5 & b \end{array}\right]-\left[\begin{array}{cc} -4 & 9 \\ c & 0.1 \end{array}\right] & =\frac{3}{5}\left[\begin{array}{cc} a & 5 \\ -35 & 1.5 \end{array}\right] \\ {\left[\begin{array}{cc} 8 & 12 \\ -20 & 4 b \end{array}\right]-\left[\begin{array}{cc} -4 & 9 \\ c & 0.1 \end{array}\right] } & =\left[\begin{array}{cc} \frac{3}{5} a & 3 \\ -21 & 0.9 \end{array}\right] \\ {\left[\begin{array}{cc} 12 & 3 \\ -20-c & 4 b-0.1 \end{array}\right] } & =\left[\begin{array}{cc} \frac{3}{5} a & 3 \\ -21 & 0.9 \end{array}\right] \end{aligned} $$
$$ \begin{aligned} &\text { Secara perbandingan, }\\ &\begin{aligned} \frac{3}{5} a & =12 \\ a & =12 \times \frac{5}{3} \\ a & =20 \end{aligned} \end{aligned} $$
$$ \begin{aligned} 4 b-0.1 & =0.9 \\ 4 b & =1 \\ b & =\frac{1}{4} \end{aligned} $$
$$ \begin{aligned} -20-c & =-21 \\ -c & =-1 \\ c & =1 \end{aligned} $$
Soalan 6:
$$ \text { Diberi }\left[\begin{array}{cc} -10 & 9 \end{array}\right]-2 X+5\left[\begin{array}{cc} 2 & 1 \end{array}\right]=\left[\begin{array}{ll} 3 & 8 \end{array}\right] \text {, hitung matriks } X \text {. } $$
Penyelesaian:
$$ \begin{aligned} {\left[\begin{array}{ll} -10 & 9 \end{array}\right]-2 X+5\left[\begin{array}{ll} 2 & 1 \end{array}\right] } & =\left[\begin{array}{ll} 3 & 8 \end{array}\right] \\ {\left[\begin{array}{ll} -10 & 9 \end{array}\right]-2 X+\left[\begin{array}{ll} 10 & 5 \end{array}\right] } & =\left[\begin{array}{ll} 3 & 8 \end{array}\right] \\ -2 X & =\left[\begin{array}{ll} 3 & 8 \end{array}\right]-\left[\begin{array}{ll} -10 & 9 \end{array}\right]-\left[\begin{array}{ll} 10 & 5 \end{array}\right] \\ -2 X & =\left[\begin{array}{ll} 3-(-10)-10 & 8-9-5 \end{array}\right] \\ -2 X & =\left[\begin{array}{ll} 3 & -6 \end{array}\right] \\ X & =-\frac{1}{2}\left[\begin{array}{ll} 3 & -6 \end{array}\right] \\ & =\left[\begin{array}{ll} -\frac{3}{2} & 3 \end{array}\right] \end{aligned} $$
$$ \text { Diberi }\left[\begin{array}{cc} -10 & 9 \end{array}\right]-2 X+5\left[\begin{array}{cc} 2 & 1 \end{array}\right]=\left[\begin{array}{ll} 3 & 8 \end{array}\right] \text {, hitung matriks } X \text {. } $$
Penyelesaian:
$$ \begin{aligned} {\left[\begin{array}{ll} -10 & 9 \end{array}\right]-2 X+5\left[\begin{array}{ll} 2 & 1 \end{array}\right] } & =\left[\begin{array}{ll} 3 & 8 \end{array}\right] \\ {\left[\begin{array}{ll} -10 & 9 \end{array}\right]-2 X+\left[\begin{array}{ll} 10 & 5 \end{array}\right] } & =\left[\begin{array}{ll} 3 & 8 \end{array}\right] \\ -2 X & =\left[\begin{array}{ll} 3 & 8 \end{array}\right]-\left[\begin{array}{ll} -10 & 9 \end{array}\right]-\left[\begin{array}{ll} 10 & 5 \end{array}\right] \\ -2 X & =\left[\begin{array}{ll} 3-(-10)-10 & 8-9-5 \end{array}\right] \\ -2 X & =\left[\begin{array}{ll} 3 & -6 \end{array}\right] \\ X & =-\frac{1}{2}\left[\begin{array}{ll} 3 & -6 \end{array}\right] \\ & =\left[\begin{array}{ll} -\frac{3}{2} & 3 \end{array}\right] \end{aligned} $$
Soalan 7:
Kedai kasut Encik Jamal menjual kasut dewasa dan kasut kanak-kanak. Jadual 1 menunjukkan stok setiap jenis kasut pada awal minggu tertentu manakala Jadual 2 menunjukkan jualan setiap jenis kasut pada minggu tersebut.
Hitung inventori akhir setiap jenis kasut pada hujung minggu tersebut. Tunjukkan pengiraan anda dalam bentuk matriks.
Penyelesaian:
$$ \begin{aligned} \text { Inventori akhir } & =\text { Inventori awal }- \text { Jualan } \\ & =\left[\begin{array}{ll} 85 & 70 \\ 110 & 98 \end{array}\right]-\left[\begin{array}{cc} 33 & 24 \\ 42 & 40 \end{array}\right] \\ & =\left[\begin{array}{ll} 52 & 46 \\ 68 & 58 \end{array}\right] \end{aligned} $$
Kedai kasut Encik Jamal menjual kasut dewasa dan kasut kanak-kanak. Jadual 1 menunjukkan stok setiap jenis kasut pada awal minggu tertentu manakala Jadual 2 menunjukkan jualan setiap jenis kasut pada minggu tersebut.
Hitung inventori akhir setiap jenis kasut pada hujung minggu tersebut. Tunjukkan pengiraan anda dalam bentuk matriks.
Penyelesaian:
$$ \begin{aligned} \text { Inventori akhir } & =\text { Inventori awal }- \text { Jualan } \\ & =\left[\begin{array}{ll} 85 & 70 \\ 110 & 98 \end{array}\right]-\left[\begin{array}{cc} 33 & 24 \\ 42 & 40 \end{array}\right] \\ & =\left[\begin{array}{ll} 52 & 46 \\ 68 & 58 \end{array}\right] \end{aligned} $$