The matrices are said to be singular if their determinant is equal to zero. For example, if we have matrix A whose all elements in the first column are zero. Then, by one of the property of determinants, we can say that its determinant is equal to zero. Hence, A would be called as singular matrix.
Note that singular matrices are non-invertible (their inverse does not exist).
As, inverse of matrix A= adj (A)/|A| …….. (1)
where adj(A) is adjoint of A and |A| is determinant of A.
If, |A|=0 (singular matrix) then inverse of matrix A will not exist according to equation (1)
Similarly, non-singular matrix is a matrix which has non-zero value of its determinant. Non-singular matrices are invertible (their inverse exist).
Taking example of matrix A equal to
From one of the property of determinants (all elements in the first row are zero which means that its determinant is equal to zero), we know that determinant of matrix A is equal to zero. Therefore A is a singular matrix.
One typical question can be asked regarding singular matrices
We are given that matrix A=
is singular. Find value of x.
Solution:
We know that determinant of singular matrix is equal to zero. Therefore determinant of A is equal to 0.
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