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If $\quad m[-3,4]+n[4-3]=[10-11], \quad$ then $3 m+7 n$ is equal to
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Verified Answer
The correct answer is:
1
Given that,
$\begin{aligned}
& m\left[\begin{array}{ll}
-3 & 4
\end{array}\right]+n\left[\begin{array}{ll}
4 & -3
\end{array}\right]=\left[\begin{array}{ll}
10 & -11
\end{array}\right] \\
\Rightarrow & {\left[\begin{array}{ll}
-3 m+4 n & 4 m-3 n
\end{array}\right]=\left[\begin{array}{ll}
10 & -11
\end{array}\right] }
\end{aligned}$
On solving equations (i) and (ii), we get $n=1, m=-2$
Now, $3 m+7 n=3(-2)+7(1)=1$
$\begin{aligned}
& m\left[\begin{array}{ll}
-3 & 4
\end{array}\right]+n\left[\begin{array}{ll}
4 & -3
\end{array}\right]=\left[\begin{array}{ll}
10 & -11
\end{array}\right] \\
\Rightarrow & {\left[\begin{array}{ll}
-3 m+4 n & 4 m-3 n
\end{array}\right]=\left[\begin{array}{ll}
10 & -11
\end{array}\right] }
\end{aligned}$
On solving equations (i) and (ii), we get $n=1, m=-2$
Now, $3 m+7 n=3(-2)+7(1)=1$
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