# rank of a matrix

Discussion in 'Math' started by sadaf, Aug 9, 2010.

Aug 4, 2010
25
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How can we find out the rank of a rectangular matrix?

Feb 4, 2008
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Use Matlab!

3. ### Papabravo Expert

Feb 24, 2006
10,340
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The rank of a matrix is the maximum number of independent rows.

For a square matrix you can compute the determinant to see if all the rows are independent. If the determinant is non-zero then the matrix is non-singular and the rank n is equal to the number of rows.

Aug 4, 2010
25
0
Ok you mean to say that we can't find the rank of a rectangular matrix or a rectangular matrix doesn't have rank.
THANX

5. ### Papabravo Expert

Feb 24, 2006
10,340
1,850

The square matrix is a special case of the rectangular matrix where the determinant can be used to determine if the rows of that square matrix are independent. Determinants don't work for rectangular matrices. So you have to use other methods to determine the maximum number of independent rows. If you reduce the rectangular matrix to row echelon form you will have your answer by inspection: counting the non-zero rows.

I trust you know what row echelon form is.

Last edited: Aug 12, 2010