Question

If $3x+2y=I$ and $2x-y=O$, where $I$ and $O$ are unit and null matrices of order $3$ respectively, then

• A. $x=\frac{1}{7},y=\frac{2}{7}$
• B. $x=\frac{2}{7},y=\frac{1}{7}$
• 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

Answer: (C)

$x=\left(\frac{1}{7}\right)I,y=\left(\frac{2}{7}\right)I$

We have,
$3x+2y=I$ ...(i)
$2x-y=O$ ....(ii)
On multiplying equation (ii) by $2$, we get
$4x-2y=2\cdot O=O$ ...(iii)
On adding equations (i) and (iii), we get
$3x+2y=I$
$4x-2y=O$
____________
$7x=I$
$\Rightarrow x=\frac{I}{7}$ or $\frac{1}{7}I$
From equation (i), we get
$2y=I-\frac{3}{7}I=\frac{4}{7}I$
$\Rightarrow y=\frac{2}{7}I$