A matrix is singular if and only if its determinant is equal to zero. The determinant is a value associated with a square matrix that can be computed using various methods, such as cofactor expansion or row reduction.

  To determine if a matrix is singular, follow these steps:

  1. Calculate the determinant of the matrix.

  2. If the determinant is equal to zero, then the matrix is singular. If the determinant is not zero, then the matrix is non-singular.

  Alternatively, you can use other properties and operations related to matrices to determine if a matrix is singular. For example:

  1. A matrix is singular if and only if its row or column vectors are linearly dependent.

  2. A square matrix is singular if and only if its rank is less than its order. The rank is the maximum number of linearly independent rows or columns in a matrix.

  3. If performing row operations on a matrix brings it to row echelon form or reduced row echelon form and there is a row of zeros, then the matrix is singular.

  These are a few ways to determine if a matrix is singular. The choice of method depends on the available information about the matrix and the computational resources available.