Singular Non-Singular Matrix :-
We determine a matrix is a singular or non-singular matrix it depends on its determinant. The determinant of a matrix A is denoted by |A| (We Call Det of A). If the determinant of a matrix is 0, then it is said to be a singular matrix.
What is a Singular Matrix?
A singular matrix is a square matrix , if the determinant of the matrix A is 0. i.e., a square matrix A is singular iff |A| = 0
Here |A| (determinant of A) is in the denominator and Adj(A) Numerator. We are know that a fraction is going to Infinite if its denominator value is 0. Hence Inverse Of A is not defined when |A|= 0. i.e., the inverse of a singular matrix is not define.
A square matrix A is said to be singular Matrix if A is follow some rules Which are given below :-
1) det A = 0 (which is also written as |A| = 0) (or)
2) A-1(Inverse of A) is NOT defined.
Properties of Singular Matrix
1) Every singular matrix is a square matrix.
2) The determinant of a singular matrix is 0.
3)A null matrix of any order is a singular matrix.
4)The inverse of a singular matrix is NOT defined and hence it is non-invertible.
5) By properties of determinants, in a matrix,
a) if any two rows or any two columns are identical, then its determinant is 0 and hence it is a singular matrix.
b) if all the elements of a row or column are zeros, then its determinant is 0 and hence it is a singular matrix.
c)if one of the rows (columns) is a scalar multiple of the other row (column) then the determinant is 0 and hence it is a singular matrix.
Non-Singular Matrix :-
A non-singular matrix is a matrix that is NOT singular i.e a square matrix A is said to be a non singular matrix if and only if det A ≠ 0. Then it is obvious that A-1 is defined.
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