# Manuals/calci/MATRIXRANK

MATRIXRANK (a)

• is any matrix.

## Description

• This function shows the rank of the Matrix.
• In  ,   is any order of the matrix.
• The Rank of the matrix is defined by maximum number of columns or Maximum number of rows in the Matrix.
• For   matrix,If   is less than  , then the maximum rank of the matrix is  .
• If   is greater than  , then the maximum rank of the matrix is  .
• Suppose all entries are zero in the given matrix then Rank of the Matrix is zero.
• If a matrix had even one non-zero element, its minimum rank would be one.

## Examples

1. MATRIXRANK(IM(9)) = 9
2. MATRIXRANK([[2,5,8,9],[3,4,6,1],[9,6,5,2]]) = 3
3. MATRIXRANK([[2,5],[8,9],[3,4],[6,1],[9,6],[5,2]]) = 2

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