Question

If the matrix equation
$\begin{bmatrix}x^{2} \\ y^{2}\end{bmatrix}-3\begin{bmatrix}x \\ 2 y\end{bmatrix}=\begin{bmatrix}-2 \\ -9\end{bmatrix}$, 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)

$\begin{bmatrix}x^{2} \\ y^{2}\end{bmatrix}-3\begin{bmatrix}x \\ 2 y\end{bmatrix}=\begin{bmatrix}x^{2}-3 x \\ y^{2}-6 y\end{bmatrix}=\begin{bmatrix}-2 \\ -9\end{bmatrix}$
Now equating the elements $x^{2}-3 x=-2$ on solving this $x =1,2$ And $y^{2}-6 y=-9$ on solving this $y=3$