Soalan 5:
$$ \text { Diberi matriks } S=\left[\begin{array}{cc} 4 x+1 & -5 \\ 6-y & x \end{array}\right], T=\left[\begin{array}{cc} x & 6 \\ 7 & 3 y \end{array}\right] \text { dan } S-T=\left[\begin{array}{cc} 10 & -11 \\ -2 & z \end{array}\right] \text {, } $$
hitung nilai x, nilai y dan nilai z.
Penyelesaian:
$$ \begin{aligned} & \text { Diberi } S-T=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right] \\ & {\left[\begin{array}{cc} 4 x+1 & -5 \\ 6-y & x \end{array}\right]-\left[\begin{array}{rr} x & 6 \\ 7 & 3 y \end{array}\right]=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right]} \\ & {\left[\begin{array}{cc} 4 x+1-x & -5-6 \\ 6-y-7 & x-3 y \end{array}\right]=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right]} \\ & {\left[\begin{array}{cc} 3 x+1 & -11 \\ -y-1 & x-3 y \end{array}\right]=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right]} \end{aligned} $$
$$ \begin{aligned} 3 x+1 & =10 \\ 3 x & =9 \\ x & =\frac{9}{3} \\ x & =3 \end{aligned} $$
$$ \begin{aligned} -y-1 & =-2 \\ -y & =-1 \\ y & =1 \end{aligned} $$
$$ \begin{array}{r} x-3 y=z \\ 3-3(1)=z \\ z=0 \end{array} $$
$$ \text { Diberi matriks } S=\left[\begin{array}{cc} 4 x+1 & -5 \\ 6-y & x \end{array}\right], T=\left[\begin{array}{cc} x & 6 \\ 7 & 3 y \end{array}\right] \text { dan } S-T=\left[\begin{array}{cc} 10 & -11 \\ -2 & z \end{array}\right] \text {, } $$
hitung nilai x, nilai y dan nilai z.
Penyelesaian:
$$ \begin{aligned} & \text { Diberi } S-T=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right] \\ & {\left[\begin{array}{cc} 4 x+1 & -5 \\ 6-y & x \end{array}\right]-\left[\begin{array}{rr} x & 6 \\ 7 & 3 y \end{array}\right]=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right]} \\ & {\left[\begin{array}{cc} 4 x+1-x & -5-6 \\ 6-y-7 & x-3 y \end{array}\right]=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right]} \\ & {\left[\begin{array}{cc} 3 x+1 & -11 \\ -y-1 & x-3 y \end{array}\right]=\left[\begin{array}{rr} 10 & -11 \\ -2 & z \end{array}\right]} \end{aligned} $$
$$ \begin{aligned} 3 x+1 & =10 \\ 3 x & =9 \\ x & =\frac{9}{3} \\ x & =3 \end{aligned} $$
$$ \begin{aligned} -y-1 & =-2 \\ -y & =-1 \\ y & =1 \end{aligned} $$
$$ \begin{array}{r} x-3 y=z \\ 3-3(1)=z \\ z=0 \end{array} $$
Soalan 6:
$$ \text { Diberi }\left[\begin{array}{cc} 3 & -4 \\ 1 & 0 \\ -6 & 7 \end{array}\right]+\left[\begin{array}{cc} -7 & 2 \\ 9 & 6 \\ 10 & 8 \end{array}\right]-V=\left[\begin{array}{cc} 11 & -4 \\ -1 & 5 \\ 6 & 9 \end{array}\right] \text {, hitung matriks } V \text {. } $$
Penyelesaian:
$$ \begin{aligned} & {\left[\begin{array}{cc} 3 & -4 \\ 1 & 0 \\ -6 & 7 \end{array}\right]+\left[\begin{array}{ll} -7 & 2 \\ 9 & 6 \\ 10 & 8 \end{array}\right]-V=\left[\begin{array}{cc} 11 & -4 \\ -1 & 5 \\ 6 & 9 \end{array}\right]} \\ & \begin{aligned} V & =\left[\begin{array}{cc} 3 & -4 \\ 1 & 0 \\ -6 & 7 \end{array}\right]+\left[\begin{array}{ll} -7 & 2 \\ 9 & 6 \\ 10 & 8 \end{array}\right]-\left[\begin{array}{cc} 11 & -4 \\ -1 & 5 \\ 6 & 9 \end{array}\right] \\ & =\left[\begin{array}{cr} 3+(-7)-11 & -4+2-(-4) \\ 1+9-(-1) & 0+6-5 \\ -6+10-6 & 7+8-9 \end{array}\right] \\ & =\left[\begin{array}{cc} -15 & 2 \\ 11 & 1 \\ -2 & 6 \end{array}\right] \end{aligned} \end{aligned} $$
$$ \text { Diberi }\left[\begin{array}{cc} 3 & -4 \\ 1 & 0 \\ -6 & 7 \end{array}\right]+\left[\begin{array}{cc} -7 & 2 \\ 9 & 6 \\ 10 & 8 \end{array}\right]-V=\left[\begin{array}{cc} 11 & -4 \\ -1 & 5 \\ 6 & 9 \end{array}\right] \text {, hitung matriks } V \text {. } $$
Penyelesaian:
$$ \begin{aligned} & {\left[\begin{array}{cc} 3 & -4 \\ 1 & 0 \\ -6 & 7 \end{array}\right]+\left[\begin{array}{ll} -7 & 2 \\ 9 & 6 \\ 10 & 8 \end{array}\right]-V=\left[\begin{array}{cc} 11 & -4 \\ -1 & 5 \\ 6 & 9 \end{array}\right]} \\ & \begin{aligned} V & =\left[\begin{array}{cc} 3 & -4 \\ 1 & 0 \\ -6 & 7 \end{array}\right]+\left[\begin{array}{ll} -7 & 2 \\ 9 & 6 \\ 10 & 8 \end{array}\right]-\left[\begin{array}{cc} 11 & -4 \\ -1 & 5 \\ 6 & 9 \end{array}\right] \\ & =\left[\begin{array}{cr} 3+(-7)-11 & -4+2-(-4) \\ 1+9-(-1) & 0+6-5 \\ -6+10-6 & 7+8-9 \end{array}\right] \\ & =\left[\begin{array}{cc} -15 & 2 \\ 11 & 1 \\ -2 & 6 \end{array}\right] \end{aligned} \end{aligned} $$
Soalan 7:
Encik Gopal mempunyai dua buah kedai, A dan B. Jadual di bawah menunjukkan pendapatan dan perbelanjaan jualan makanan dan minuman bagi kedua-dua buah kedainya pada bulan Jun.
Hitung jumlah keuntungan yang diperoleh Encik Gopal dari setiap kedainya pada bulan Jun. Tunjukkan pengiraan anda dalam bentuk matriks.
[Diberi bahawa keuntungan = pendapatan – perbelanjaan]
Penyelesaian:
$$ \begin{aligned} & {\left[\begin{array}{l} 2650 \\ 1560 \end{array}\right]+\left[\begin{array}{c} 1890 \\ 910 \end{array}\right]-\left[\begin{array}{l} 930 \\ 540 \end{array}\right]-\left[\begin{array}{l} 850 \\ 260 \end{array}\right]} \\ & =\left[\begin{array}{c} 2650+1890-930-850 \\ 1560+910-540-260 \end{array}\right] \\ & =\left[\begin{array}{c} 2760 \\ 1670 \end{array}\right] \end{aligned} $$
Maka, keuntungan dari Kedai A dan Kedai B ialah RM 2760 dan RM 1670 masing-masing.
Encik Gopal mempunyai dua buah kedai, A dan B. Jadual di bawah menunjukkan pendapatan dan perbelanjaan jualan makanan dan minuman bagi kedua-dua buah kedainya pada bulan Jun.
Hitung jumlah keuntungan yang diperoleh Encik Gopal dari setiap kedainya pada bulan Jun. Tunjukkan pengiraan anda dalam bentuk matriks.
[Diberi bahawa keuntungan = pendapatan – perbelanjaan]
Penyelesaian:
$$ \begin{aligned} & {\left[\begin{array}{l} 2650 \\ 1560 \end{array}\right]+\left[\begin{array}{c} 1890 \\ 910 \end{array}\right]-\left[\begin{array}{l} 930 \\ 540 \end{array}\right]-\left[\begin{array}{l} 850 \\ 260 \end{array}\right]} \\ & =\left[\begin{array}{c} 2650+1890-930-850 \\ 1560+910-540-260 \end{array}\right] \\ & =\left[\begin{array}{c} 2760 \\ 1670 \end{array}\right] \end{aligned} $$
Maka, keuntungan dari Kedai A dan Kedai B ialah RM 2760 dan RM 1670 masing-masing.