If $m [- 34] + n [4 - 3] = [10 - 11],$ then $3 m + 7 n =$

3

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5

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10

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1

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Solution

The correct option is C $1$
Given, $m [\begin{matrix} - 3 & 4 \end{matrix}] + n [\begin{matrix} 10 & - 11 \end{matrix}] = [\begin{matrix} 10 & - 11 \end{matrix}]$
$\Rightarrow [\begin{matrix} - 3 m + 4 n & 4 m - 3 n \end{matrix}] = [\begin{matrix} 10 & - 11 \end{matrix}]$
By equating above matrices, we get
$- 3 m + 4 n = 10 ⟹ 12 m - 16 n = - 40$ ........(1)
$4 m - 3 n = - 11 ⟹ 12 m - 9 n = - 33$ ........(2)
Solving equation (1) and (2), we get,
$n = 1$ and $m = - 2$
Therefore,
$3 m + 7 n = 3 (- 2) + 7 = - 6 + 7 = 1$

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