finding number of submatrices of a matrix of given order?

Question

How do we calculate the number of possible submatrices of a matrix of order $5\times 6$?

options for the answer are:

What data characterise a submatrix? – Daniel Fischer Sep 05 '14 at 15:32 — Daniel Fischer, Sep 05 '14 at 15:32

score 4 · Answer 1 · answered Sep 05 '14 at 15:32

4

Hint: select a subset of rows and then a subset of columns. Empty sets are not allowed.

answered Sep 05 '14 at 15:32

Robert Israel

it is given 31*63=1953 in the book in which i read.but i dint understand this? can anyone explain me this? – amit Sep 05 '14 at 15:35
1

There are $2^5 = 32$ subsets of the $5$ rows, but the empty set is not allowed, so that leaves $31$. Similarly for the columns. – Robert Israel Sep 05 '14 at 15:41
yeah i got it..thanks – amit Sep 06 '14 at 04:39

1 Answers1