Question 13 Marks
In $\left[\begin{array}{cc}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$ find the value of $x, y, z$ ?
Answer
View full question & answer→$\begin{array}{r}\text{On comparing}\ x+y=6 \\
5+z=5 \\
x y=8
\end{array}$
from equation (1) and (3)
$\begin{array}{rlrl} x(6-x) =8 \\ \Rightarrow \quad 6 x-x^2 & =8 \\ \Rightarrow \quad x^2-6 x+8 & =0 \\ \Rightarrow x^2-4 x-2 x+8 & =0 \end{array}$
$\begin{aligned}
\Rightarrow & & x(x-4)-2(x-4) & =0 \\
\Rightarrow & & (x-4)(x-2) & =0 \\
\Rightarrow & & x & =4,2
\end{aligned}$
$\begin{array}{l}\text { when } x=4, y=6-x=6-4=2 \\ \text { when } x=2, y=6-2=4\end{array}$
from equation (2), $z=0$
5+z=5 \\
x y=8
\end{array}$
from equation (1) and (3)
$\begin{array}{rlrl} x(6-x) =8 \\ \Rightarrow \quad 6 x-x^2 & =8 \\ \Rightarrow \quad x^2-6 x+8 & =0 \\ \Rightarrow x^2-4 x-2 x+8 & =0 \end{array}$
$\begin{aligned}
\Rightarrow & & x(x-4)-2(x-4) & =0 \\
\Rightarrow & & (x-4)(x-2) & =0 \\
\Rightarrow & & x & =4,2
\end{aligned}$
$\begin{array}{l}\text { when } x=4, y=6-x=6-4=2 \\ \text { when } x=2, y=6-2=4\end{array}$
from equation (2), $z=0$