The number of matrices of order 3 times 3, wh | vedclass

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Question

$A =\left[\begin{array}{lll} a _{11} & a _{12} & a _{13} \ a _{21} & a _{22} & a _{23} \ a _{31} & a _{32} & a _{33}\end{arr

Vedclass · Accepted Answer

$282$

Vedclass · Answer

$A =\left[\begin{array}{lll} a _{11} & a _{12} & a _{13} \ a _{21} & a _{22} & a _{23} \ a _{31} & a _{32} & a _{33}\end{array}ight] a _{ ij } \in\{0,1\}$

$\sum a_{i j}=2,3,5,7$

Total matrix $={ }^{9} C _{2}+{ }^{9} C _{3}+{ }^{9} C _{5}+{ }^{9} C _{7}$

$=282$

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

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