On the other hand, a non-singular matrix is a matrix whose determinant is NOT 0 and hence it has an inverse. What are Singular and Non Singular Matrices?Ī singular matrix is a matrix whose determinant is 0 and hence it has no inverse. Then the rank of the matrix is definitely less than the order of the matrix. If A is a singular matrix of order n, then it means that det A = 0. If there is no matrix B such that AB = BA = I, then it means that A has no inverse and in this case also, A is said to be singular. If the determinant of A is 0 then A is singular. If 'A' is non singular then the system of simultaneous equations AX = B has a unique solution.Įxample: \(\left\) is singular as its determinant is zero (as its first and third rows are equal). If 'A' is singular then the system of simultaneous equations AX = B has either no solution or has infinitely many solutions. Some rows and columns are linearly dependent.Īll rows and columns are linearly independent. If 'A' is nonsingular then A -1 is defined. If 'A' is singular then A -1 is NOT defined. Thus, we can summarize the differences between the singular matrix and non-singular matrix as follows:Ī matrix 'A' is nonsingular if det (A) ≠ 0. ![]() i.e., a non-singular matrix always has a multiplicative inverse. ![]() i.e., a square matrix 'A' is said to be a non singular matrix if and only if det A ≠ 0. Thus, the determinant of a non-singular matrix is a nonzero number. A non-singular matrix, as its name suggests, is a matrix that is NOT singular.
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