![]() ![]() Then use some algebra to solve for $ y $. For Matrix $ C $ to be singular, we have to equate the determinant equation to $ 0 $.Now, calculating the determinant for Matrix $ B$: If it’s $ 0 $, then it is a singular matrix. We check the determinant of each matrix.Singular matrices are square matrices whose determinant is $ 0 $. Determinant of a Singular Matrixįrom the definition of a singular matrix, we know that a singular matrix’s determinant is ZERO! 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. Matrices whose determinant is $ 0 $ are called singular matrices, and matrices whose determinant is non-zero are called non-singular matrices. A non-singular matrix, as its name suggests, is a matrix that is NOT singular. A singular matrix is also known as a degenerate. Since the determinant is $ 0 $, we can’t find the inverses of such matrices. Simply put, a singular matrix is a matrix whose determinant is $ 0 $. In this lesson, we will discover what singular matrices are, how to tell if a matrix is singular, understand some properties of singular matrices, and the determinant of a singular matrix. Let’s check the formal definition of a singular matrix:Ī matrix whose determinant is $ 0 $ and thus is non-invertible is known as a singular matrix. But for this topic, we will look at it from a much lower level of mathematics. Though simple, it has immense importance in linear transformations and higher-order differential equations. ![]() ![]() A singular matrix is a very simple matrix. ![]()
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