QJEEM23Ma7591: JEE Main 2023 Mathematics - Class 11 JEEM23Ma7591 Solution: Let . The number of matrices A such that the sum of all entries …

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Such that $\Sigma a_{i i}=3,5,7$ or 11

Then for sum 3, the possible entries are $(0,0,0,3)$ , $(0,0,1,2),(0,1,1,1)$ .

Then total number of possible matrices $$=4+12+4$$ $=20$

For sum 5 the possible entries are $(0,0,1,4)$ , $(0,0,2,3),(0,1,2,2),(0,1,1,3)$ and $(1,1,1,2)$ .

$\therefore$ Total possible matrices $=12+12+12+12+4=52$

For sum 7 the possible entries are $(0,0,3,4)$ , $(0,2,2,3),(0,1,2,4),(0,1,3,3),(1,2,2,2)$ , $(1,1,2,3)$ and $(1,1,1,4)$ .

$\therefore$ Total possible matrices $=80$

For sum 11 the possible entries are $(0,3,4,4)$ , $(1,2,4,4),(2,3,3,3),(2,2,3,4)$ .

$\therefore$ Total number of matrices $=52$

$\therefore$ Total required matrices $=20+52+80+52$ $$=204$$