How many matrices
Algebra
Level
pending
Find the number of different symmetric matrices with each element being 0 or 1.
64
16
65536
1024
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1 solution
The four diagonal elements can fill with 0 and 1 with 2^4 ways.Since matrix is symmetrical upper triangular matrix elements and lower triangular matrix elements are same.So we have to freedom to fill these 6 places.These place fill with 0 and 1 with 2^6 ways. So total number of ways fill 4×4 symmetrical matrix with 0 and 1 is 2^4*2^6=2^10=1024