Question

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

• A. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)$
• B. $X=\left(\frac{2}{7}\right),Y=\left(\frac{1}{7}\right)I$
• C. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)I$
• D. $X=\left(\frac{2}{7}\right)I,Y=\left(\frac{1}{7}\right)I$

Answer 1

The correct option is C

$X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)I$

$\begin{array}{cc}& 3X+2Y=I\\ & 2X-Y=0\end{array}\Rightarrow \begin{array}{cc}& 3X+2Y=I\\ & 4X-2Y=0\end{array}\Rightarrow \begin{array}{cc}& 7X=I\\ & X=\frac{1}{7}I\end{array}$
(Solving simultaneously)
Therefore from (i), $2Y=I-\frac{3}{7}I=\frac{4}{7}I\Rightarrow Y=\frac{2}{7}I$