Question

If the matrix equation
$\left[\begin{array}{c}{x}^2\\ y^2\end{array}\right]-3\left[\begin{array}{c}x\\ 2y\end{array}\right]=\left[\begin{array}{c}-2\\ -9\end{array}\right]$, then the values of $x$ and $y$ are

• A. (1,3)
• B. (2,3)
• C. both (a) & (b)
• D. None of these

Answer 1

Answer: (C)

$\left[\begin{array}{c}{x}^2\\ y^2\end{array}\right]-3\left[\begin{array}{c}x\\ 2y\end{array}\right]=\left[\begin{array}{c}{x}^2-3x\\ y^2-6y\end{array}\right]=\left[\begin{array}{c}-2\\ -9\end{array}\right]$
Now equating the elements $x^2-3x=-2$ on solving this $x=1,2$ And $y^2-6y=-9$ on solving this $y=3$