If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then Options: A . &nbspX=(17),Y=(27) B . &nbspX=(27),Y=(17) C . &nbspX=(17)I,Y=(27)I D . &nbspX=(27)I,Y=(17)I

Answer: Option C : C 3 X + 2 Y = I 2 X − Y = 0 ⇒ 3 X + 2 Y = I 4 X − 2 Y = 0 ⇒ 7 X = I X = 1 7 I (Solving simultaneously) Therefore from (i), 2 Y = I − 3 7 I = 4 7 I ⇒ Y = 2 7 I

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matric

Question

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

Options:

A . X=(17),Y=(27)

B . X=(27),Y=(17)

C . X=(17)I,Y=(27)I

D . X=(27)I,Y=(17)I

Answer: Option C
:
C

\begin{matrix} 3 X + 2 Y = I 2 X - Y = 0 \end{matrix} \Rightarrow \begin{matrix} 3 X + 2 Y = I 4 X - 2 Y = 0 \end{matrix} \Rightarrow \begin{matrix} 7 X = I X = \frac{1}{7} I \end{matrix}

(Solving simultaneously)
Therefore from (i),

2 Y = I - \frac{3}{7} I = \frac{4}{7} I \Rightarrow Y = \frac{2}{7} I

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