Question

Solve the matrix equation $\left[\begin{array}{c}{x}^2\\ y^2\end{array}\right]-3\left[\begin{array}{c}x\\ 2y\end{array}\right]=\left[\begin{array}{c}-2\\ 9\end{array}\right]$

Answer 1

Given,
$\left[\begin{array}{c}{x}^2\\ y^2\end{array}\right]-3\left[\begin{array}{c}x\\ 2y\end{array}\right]=\left[\begin{array}{c}-2\\ 9\end{array}\right]$
$\Rightarrow \left[\begin{array}{c}{x}^2-3x\\ y^2-6y\end{array}\right]=\left[\begin{array}{c}-2\\ 9\end{array}\right]$
$\Rightarrow x^2-3x=-2and{y}^2-6y=9$
By solving, we get
$x=1$ or $2$ and $y=3\pm 3\sqrt{2}$