Question

What is the rank of a singular matrix?

Answer 1

Singular Matrix:

• A singular matrix is an arrangement of elements in rows and columns in a square form, whose determinant is $0$.
• In a singular matrix, all the rows and columns are not unique. So, the least number of unique rows and columns determines the rank of the matrix.
• Assume, there is a $\mathrm{m}\times \mathrm{m}$ singular matrix, then its rank should be less than or equal to $\mathrm{m}$.

Hence, the rank of singular matrix is less than number of row/column.