If 3[4213]−2[−2132]+[x−43y]=0 , then (x,y)=

3[4213]−2[−2132]+[x−43y]=0 ⇒[12639]−[−4264]+[x−43y]=0 ⇒12−(−4)+x=0 ⇒12+4+x=0 ⇒x=−16 9−4+y=0 ⇒y=−5 ∴(−16,−5)

If 3[4213]−2[−2132]+[x−43y]=0 , then (x,y)=

3[4213]−2[−2132]+[x−43y]=0 ⇒[12639]−[−4264]+[x−43y]=0 ⇒12−(−4)+x=0 ⇒12+4+x=0 ⇒x=−16 9−4+y=0 ⇒y=−5 ∴(−16,−5)

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If $3 [\begin{matrix} 4 & 2 \\ 1 & 3 \end{matrix}] - 2 [\begin{matrix} - 2 & 1 \\ 3 & 2 \end{matrix}] + [\begin{matrix} x & - 4 \\ 3 & y \end{matrix}] = 0$ , then $(x, y) =$

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(16 5)

(5 16)

(- 16 - 5)

(- 5 - 16)

answer is C.

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Detailed Solution

3 [\begin{matrix} 4 & 2 \\ 1 & 3 \end{matrix}] - 2 [\begin{matrix} - 2 & 1 \\ 3 & 2 \end{matrix}] + [\begin{matrix} x & - 4 \\ 3 & y \end{matrix}] = 0

$\Rightarrow [\begin{matrix} 12 & 6 \\ 3 & 9 \end{matrix}] - [\begin{matrix} - 4 & 2 \\ 6 & 4 \end{matrix}] + [\begin{matrix} x & - 4 \\ 3 & y \end{matrix}] = 0$

$\Rightarrow 12 - (- 4) + x = 0$

$\Rightarrow 12 + 4 + x = 0$

$\Rightarrow x = - 16$

$9 - 4 + y = 0$

$\Rightarrow y = - 5$

$∴ (- 16, - 5)$

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If 3[4213]−2[−2132]+[x−43y]=0 , then (x,y)=

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If $3 [\begin{matrix} 4 & 2 \\ 1 & 3 \end{matrix}] - 2 [\begin{matrix} - 2 & 1 \\ 3 & 2 \end{matrix}] + [\begin{matrix} x & - 4 \\ 3 & y \end{matrix}] = 0$ , then $(x, y) =$