Eigenvalue:
In a linear system of equations, eigenvalues are actually special set of scalars which are associated with these equations.
Singular Matrix:
A matrix whose determinant is Zero is called singular matrix.
Step-by-step explanation:
[tex]Let A = \left[\begin{array}{ccc}a1&a2&a3\\a4&a5&a6\\a7&a8&a9\end{array}\right][/tex]
[tex]Identity Matrix = I = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
.
If Matrix A is singular it means that
det (A) = 0
det (A-0.I)=0
because [tex]0*\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right][/tex]
So,
det (A-0.I) = 0 implies that 0 is eigenvalue of matrix A.
