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  4. If m[-3,4]+n[4-3]=[10-11], then 3 m+7 n is equal to

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Q. If $m[-3,4]+n[4-3]=[10-11]$, then $3 m+7 n$ is equal to

EAMCETEAMCET 2005

Solution:

Given that,
$m[-3 \,\, 4]+n[4 -3]=[10 -11]$
$\Rightarrow [-3 m+4 n\,\, 4 m-3 n]=[10 -11]$
$\Rightarrow -3 m+4 n=10\,\,\,....(i)$
and $ 4 m-3 n=-11\,\,\,....(ii)$
On solving equations (i) and (ii), we get
$n=1, \,m=-2$
Now, $3 m+7 n=3(-2)+7(1)=1$