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How may ways can you partition a 3x3 matrix?

How may ways can you partition a 3x3 matrix?
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Answer #1

A 3×3 matrix has 9 elements. The number of partitions of the matrix can be found by finding the the number of ways in which the number 9 can be written as a sum of positive integers.

9 can be written as a sum of positive integers in 30 ways. See the image below.

Therefore, a 3×3 matrix has 30 partitions.

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