**The number of matrices of order 3 * 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is……….**

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7 months ago

$A = [\begin{matrix} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{matrix}], a_{2}, b_{2}, c_{2} \in {0, 1}$

S = $a_{1} + a_{2} + a_{3} + b_{1} + b_{2} + b_{3} + c_{1} + c_{2} + c_{3}$ is prime

$0 \leq s \leq 9$

Prime value = 2,3, 5, 7

$F o r S = 2, 1 + 1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 \to \frac{9!}{2! 7!} = 36$

Total number of matrices

= 36 + 84 + 126 + 36 = 282

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