Soalan 3:
$$ \text { Diberi }\left[\begin{array}{cc} -1 & x \\ y & 3 \end{array}\right]\left[\begin{array}{l} 4 \\ 7 \end{array}\right]=\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \text {, hitung nilai } x \text { dan nilai } y \text {. } $$
Penyelesaian:
$$ \begin{aligned} {\left[\begin{array}{cc} -1 & x \\ y & 3 \end{array}\right]\left[\begin{array}{l} 4 \\ 7 \end{array}\right] } & =\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \\ {\left[\begin{array}{c} (-1) 4+x(7) \\ y(4)+3(7) \end{array}\right] } & =\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \\ {\left[\begin{array}{c} 7 x-4 \\ 4 y+21 \end{array}\right] } & =\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \end{aligned} $$
$$ \begin{aligned} &\text { Bandingkan unsur-unsur sepadan, }\\ &\begin{aligned} 7 x-4 & =31 \\ 7 x & =35 \\ x & =5 \end{aligned}\\ &\begin{aligned} 4 y+21 & =29 \\ 4 y & =8 \\ y & =2 \end{aligned} \end{aligned} $$
$$ \text { Diberi }\left[\begin{array}{cc} -1 & x \\ y & 3 \end{array}\right]\left[\begin{array}{l} 4 \\ 7 \end{array}\right]=\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \text {, hitung nilai } x \text { dan nilai } y \text {. } $$
Penyelesaian:
$$ \begin{aligned} {\left[\begin{array}{cc} -1 & x \\ y & 3 \end{array}\right]\left[\begin{array}{l} 4 \\ 7 \end{array}\right] } & =\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \\ {\left[\begin{array}{c} (-1) 4+x(7) \\ y(4)+3(7) \end{array}\right] } & =\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \\ {\left[\begin{array}{c} 7 x-4 \\ 4 y+21 \end{array}\right] } & =\left[\begin{array}{l} 31 \\ 29 \end{array}\right] \end{aligned} $$
$$ \begin{aligned} &\text { Bandingkan unsur-unsur sepadan, }\\ &\begin{aligned} 7 x-4 & =31 \\ 7 x & =35 \\ x & =5 \end{aligned}\\ &\begin{aligned} 4 y+21 & =29 \\ 4 y & =8 \\ y & =2 \end{aligned} \end{aligned} $$
Soalan 4:
$$ \text { Diberi }\left[\begin{array}{cc} 9 & r \\ 5 & -2 \end{array}\right]\left[\begin{array}{ll} 4 & s \\ 6 & 1 \end{array}\right]=\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \text {, hitung nilai } r \text { dan nilai } s \text {. } $$
Penyelesaian:
$$ \begin{aligned} {\left[\begin{array}{cc} 9 & r \\ 5 & -2 \end{array}\right]\left[\begin{array}{ll} 4 & s \\ 6 & 1 \end{array}\right] } & =\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \\ {\left[\begin{array}{cc} 9(4)+r(6) & 9(s)+r(1) \\ 5(4)+(-2) 6 & 5(s)+(-2) 1 \end{array}\right] } & =\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \\ {\left[\begin{array}{cc} 6 r+36 & 9 s+r \\ 8 & 5 s-2 \end{array}\right] } & =\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \end{aligned} $$
$$ \begin{aligned} &\text { Bandingkan unsur-unsur sepadan, }\\ &\begin{aligned} 6 r+36 & =15 \\ 6 r & =-21 \\ r & =-3.5 \end{aligned}\\ &\begin{aligned} 5 s-2 & =8 \\ 5 s & =10 \\ s & =2 \end{aligned} \end{aligned} $$
$$ \text { Diberi }\left[\begin{array}{cc} 9 & r \\ 5 & -2 \end{array}\right]\left[\begin{array}{ll} 4 & s \\ 6 & 1 \end{array}\right]=\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \text {, hitung nilai } r \text { dan nilai } s \text {. } $$
Penyelesaian:
$$ \begin{aligned} {\left[\begin{array}{cc} 9 & r \\ 5 & -2 \end{array}\right]\left[\begin{array}{ll} 4 & s \\ 6 & 1 \end{array}\right] } & =\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \\ {\left[\begin{array}{cc} 9(4)+r(6) & 9(s)+r(1) \\ 5(4)+(-2) 6 & 5(s)+(-2) 1 \end{array}\right] } & =\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \\ {\left[\begin{array}{cc} 6 r+36 & 9 s+r \\ 8 & 5 s-2 \end{array}\right] } & =\left[\begin{array}{cc} 15 & 14.5 \\ 8 & 8 \end{array}\right] \end{aligned} $$
$$ \begin{aligned} &\text { Bandingkan unsur-unsur sepadan, }\\ &\begin{aligned} 6 r+36 & =15 \\ 6 r & =-21 \\ r & =-3.5 \end{aligned}\\ &\begin{aligned} 5 s-2 & =8 \\ 5 s & =10 \\ s & =2 \end{aligned} \end{aligned} $$