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In an M × N  matrix all non-zero entries are covered in  rows and  columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In an M × Nmatrix all non-zero entries are covered in rows and c...
maximum number of non-zero entries, such that no two are on the same row or column
Any entry will be a member of some row and some column. So, with  rows we can have maximum  elements such that no row has a repeated element. Same is applicable for b columns also. So, combining both, answer should be .
We can also apply pigeonhole principle here. Let
P = min(a.b) be the number of holes. So, we can place up to
P non-zero entries (pigeons) and as soon as
(P + 1)th entry comes it must be making two entries in some column or row. 
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In an M × Nmatrix all non-zero entries are covered in rows and columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, isa)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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