2.2.1 Matriks Sama (Contoh Soalan)

2.2.1 Matriks Sama (Contoh Soalan)

Contoh 1:

$(\begin{matrix} 1 & x + 2 \\ 4 - y & - 1 \end{matrix}) = (\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix})$

Penyelesaian:

$\begin{array}{l} (\begin{matrix} 1 & x + 2 \\ 4 - y & - 1 \end{matrix}) = (\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix}) \\ x + 2 = 3 \\ x = 1 \\ 4 - y = 2 \\ - y = - 2 \\ y = 2 \end{array}$

Contoh 2:

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

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

Penyelesaian:

$(a) (\begin{matrix} 3 & 2 p + q \\ p & - 3 \end{matrix}) = (\begin{matrix} 3 & 1 \\ 8 - 2 q & - 3 \end{matrix})$
2p + q = 1

q = 1 – 2p ----(1)

p = 8 – 2q ----(2)

Gantikan (1) ke dalam (2),

p = 8 – 2 (1 – 2p)

p = 8 – 2 + 4p

p – 4p = 6

–3p = 6

p = –2

Gantikan p = –2 ke dalam (1),

q = 1 – 2(–2)

q = 5

$(b) (\begin{matrix} 10 & 0 \\ 5 p - 8 & 1 \end{matrix}) = (\begin{matrix} p - 2 q & 0 \\ - 4 q & 1 \end{matrix})$
10 = p – 2q

p = 10 + 2q ----(1)

5p – 8 = –4q ----(2)

Gantikan (1) ke dalam (2),

5 (10 + 2q) – 8 = –4q

50 + 10q – 8 = –4q

14q = –42

q = –3

Gantikan q = –3 ke dalam (1),

p = 10 + 2(–3)

p = 4

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